chapter 3 removal of hrv artifacts using adaptive...
TRANSCRIPT
56
CHAPTER 3
REMOVAL OF HRV ARTIFACTS USING ADAPTIVE
THRESHOLD RANK ORDER FILTER
3.1 INTRODUCTION
Any artifact in the HRV series may interfere with analysis of the
signal. The artifacts within HRV signals can be divided into technical and
physiological artifacts. The technical artifacts can include missing or
additional QRS complex detections and error in R-wave occurrence time.
These artifacts may be due to measurement artifacts or the computational
algorithm. The physiological artifacts, on the other hand, include Ectopic
beats and arrhythmic events. In order to avoid the interference of such
artifacts only artifact-free sections are included in the HRV analysis.
There are two main arguments for the removal of ectopic beats
from the HRV signal prior to the calculation of HRV metrics. First, heart rate
modulatory signals involving the ANS and cardio-vascular systems act upon
the sinoatrial (SA) node in the heart, influencing sinus rhythm. Assessments
of autonomic function reflect the ability of the system to stimulate the SA
node. Ectopic beats originate from secondary and tertiary pacemakers and this
type of locally aberrant beat will temporarily disrupt normal neurocardiac
modulation. Second, an ectopic beat will often appear late or early with
respect to the timing of a sinus beat, creates a sharp spike in the HRV series,
likely to add a significant power contribution to the power spectrum at an
artifactual frequency. There exist algorithms which can detect and classify
57
ectopic beats, but for HRV analysis these beats are removed either by manual
editing or by some means of filtering and interpolation.
3.2 DETECTION AND CORRECTION OF ARTIFACTS
The simple artifact detection criteria include absolute upper
(2.0 secs) and lower (0.3 secs) limits for acceptable RR interval variations and
intervals less than or equal to 80% of the previous sinus cycle length. Two
basic procedures mainly used for removing the individual artifacts from the
RR interval time series are:
1. Total exclusion of abnormal intervals
2. Substitution of a better matching value
The exclusion approach suits well for time domain and frequency
domain analysis if only a few beats are to be excluded, whereas if more beats
have to be processed, the substitution approach is used widely with both time
and frequency domain analysis. The substitution approaches can take the form
of simply replacing the abnormal value with a local mean or median,
neighbourhood values or low pass interpolated values.
3.3 DISCRETE WAVELET TRANSFORM BASED METHODS
Conventionally, ectopic beats are corrected manually. Keenan
(2006) developed a discrete wavelet threshold based interpolation method for
detecting and correcting ectopic beats automatically. In this method, Ectopic
beats are first identified and corrected by one level DWT and then 2 beat
cycles are low pass interpolated to create a smooth signal. Wavelet threshold
based filters are spatially adaptive; suits well for preprocessing non-stationary
signals. The very appealing feature of wavelet analysis is that it gives uniform
resolution for all scales. This feature is very useful for analyzing signals
58
which undergo gradual frequency changes. The nonlinear feature of HRV
allows sudden changes which may lead to leakage of power due to the limited
length of the basic wavelet function. The main issue in wavelet based method
is how to choose a wavelet function, level of wavelet decomposition and an
optimal threshold which can be adaptive to the complexity of HRV signals.
The efficiency of the method depends on the following three conditions:
1. The suitability of wavelet function for the multifunctional
multicomponent HRV signals.
2. The level of wavelet decomposition to preserve the VLF
variations of HRV for further analysis and
3. Selection of optimal threshold conditions.
The HRV signal has wide range of frequency variations
(0.5 Hz to 0.001 Hz). The required level of wavelet decomposition is
unknown prior to analysis. Moreover, increasing the level of decomposition
may increase the number of wavelet coefficients thereby the computational
complexity of the method. If less number of decomposition levels are
preferred then there is a possibility of losing some of the LF and VLF
variations of the HRV signals. The above features make the wavelet threshold
based filters less adaptive to the multifunctional multicomponent nature of
HRV signals.
3.4 ADAPTIVE RANK ORDER FILTER
The rank order filter is a nonlinear filter which processes the data
sample by sample and do not assume any functional forms, linear and
stationary conditions in the HRV series. The filter replaces the noisy beats
captured by the optimal threshold conditions by the rank value. Hence it
59
preserves the LF and VLF variations for further HRV analysis. The input
output relationship of the rank order filter is given by Equation (3.1).
yr(n)=rth
rank [x(n-N), x(n-N+1), …., x(n), ….,x(n+N-1), x(n+N)] (3.1)
where r = 1,2, …..2N + 1. The window size of the filter is W=2N+1.
Two types of adaptations are incorporated into the Adaptive Rank
Order Filter.
1. Adaptive filtering output
2. Adaptive window size
For the aspect of adaptive filtering output, the output may be a
noise free median (rank value) or a noise free non-median which is then used
to replace the center element in the window, W. As for the adaptive window
size, a window expansion scheme is adopted where the criterion to expand
window is, that all the elements within the current window are noisy. The
window width varies from 3 to 7 and N is the number of samples.
Let x and B represent the input and output vectors and a1 is the
lower threshold (0.3 secs) and a2 is the upper threshold (2.0 secs). The AROF
algorithm is
i = centre {xi to s | s W} ; W ={s | -n < s <+n }; n=(N-1)/2;
i = median {xj to s | s W} and
i = non-median {xj to s | s W}; where xj = [x1 x2 x3 …… xs];
B(i) = i : if |a1 < i < a2| or
B(i) = i : if |a1 < i < a2| or
B(i) = i : if |a1 < i < a2|
Otherwise expand the window size W.
60
3.5 ADAPTIVE THRESHOLD RANK ORDER FILTER
The Adaptive Threshold Rank Order Filter (ATROF) is an
extension of AROF. Three types of adaptations are incorporated into the rank
order filter to form ATROF which are
1. Adaptive filtering output
2. Adaptive window size
3. Adaptive Thresholds
The adaptive window size and adaptive filtering conditions are
similar to AROF. For the aspect of adaptive thresholds, the upper and lower
threshold conditions (ai) for the current window are updated based on the
previous window non noisy value.
ai ={B(i-1) + 0.20* B(i-1) if i = 1 otherwise
B(i-1) - 0.20* B(i-1) if i= 2}:
where B (i-1) is previous window non-noisy sample value with ± 20%
tolerance of non noisy sample value. The initial threshold conditions are
assumed either based on the standard deviation of the signal or the non noisy
first sample value of the time series. The adaptive threshold conditions make
the approach completely automatic and tracks the LF and VLF variations of
the HRV signals.
3.5.1 Procedural Steps
Given a noisy signal A and initial window size 3, the ATROF is
implemented as follows:
Step 1: Duplicate the noisy input signal to an output variable B. Set the
initial value of the threshold ai =fint ± 0.2(fint) is based on the initial
non noisy sample value of the signal.
61
Step 2: Check if the center element in the window is noisy or not. If yes
then go to step 3. Otherwise, update the threshold value by the
center element, ai = i ± 0.2( i) and move the center of the window
to the next element and redo step 2.
Step 3: Sort all the elements within the window in the ascending order and
find the median i.
Step 4: Determine if i is noisy or not using the threshold conditions. If yes
then jump to step 6. Otherwise, the median i is non-noisy and go to
step 5.
Step 5: Replace the corresponding center element in the output B with i,
update the new threshold, ai = i ±0.2( i) and go to step 6.
Step 6: Check if all other elements (non median i) within the window are
noisy or not. If yes, then expand the window size and go back to
step 2. Otherwise, go to step 7.
Step 7: Replace the corresponding center element in output B with the
noise free non median ( i). Set the new threshold, ai = i ±0.2( i)
Step 8: Reset window size and move the center of the window to next
element.
Step 9: Repeat the steps until all the elements are processed.
3.5.2 PSD Estimation
Methods for PSD estimation can be classified as nonparametric
methods based on Fast Fourier Transform and parametric methods based on
autoregressive (AR) time series modeling. In the latter approach, the HRV
time series is modeled as an AR(p) process
62
p
t j t j tj 1
z a z e ,t p 1,.......N 1 (3.2)
where p (p=21) is the model order, aj are the AR coefficients, and et is the
noise term. A modified covariance method is used to solve the AR model
equation. The power spectrum estimate Pz is then calculated as
2
z 2p
i jj
j 1
P ( )
1 a e
(3.3)
where 2 is the variance of the prediction error of the model. In this work, for
spectrum estimations, free HRV analysis software (Developed by biomedical
signal analysis group, Department of Applied Physics, University of Kuopio,
Finland) has been used.
3.6 EXPERIMENTAL RESULTS
3.6.1 Effect of Ectopic Beats on Simulated Signals
To study the effect of ectopic beats at different magnitude levels
and rise in number of ectopic beats, a simulation study has been formulated.
For the simulation of RR intervals, Integral Pulse Frequency Modulator
(IPFM) is used to model the neural modulation of the SA-node. According to
this model, the input signal (mo+ m(t)), which involves a DC component (mo)
and a modulating sinusoidal component (m(t)) are integrated and, whenever
the integrated value exceeds a fixed threshold R, a unitary spike is generated,
and the integrator is reinitialized. For spectrum estimation the event series is
interpolated to a continuous time series. The modulating sinusoidal input m
(t), involves only two components to simulate the influences of the two ANS
activities, m(t)=Al cos (2 fl)t +Ah cos (2 fh)t. Al and Ah are the amplitudes
and fl and fh are the frequencies of the low (LF) and high (HF) frequency
63
components of the signal. The low frequency (LF) occurs in a band between
0.4 Hz and 0.15 Hz, provides a measure of sympathetic effect on the heart
rate. The high frequency component (HF) defined between 0.15 and 0.4 Hz
provides a measure of cardiac parasympathetic activity. The ratio of power LF
to HF bands (LF/HF) provides the measure of cardiac sympathovagal balance.
To evaluate the effect of ectopy on HRV metrics, artificial ectopic
beats are added to an RR interval tachogram using the procedure described by
Kamath et al (1995). Ectopic beats are defined in terms of timing, as those
which have intervals less than or equal to 80% of the previous sinus cycle
length. Each data in the RR interval tachogram represents an interval between
two beats and the insertion of an ectopic beat therefore corresponds to the
replacement of two data points as follows. The nth and (n+1)th beats (where n
is chosen randomly) are replaced by
'n n 1RR RR (3.4)
' 'n 1 n 1 n nRR RR RR RR (3.5)
where the ectopic beat’s timing is the fraction ( 0.8) of the previous RR
interval. Figures 3.1 (a) and (b) show the simulated signal and its spectrum.
0 50 100 150 200 250 3000.5
1
1.5
2
2.5
Simulated ectopic signal
Time (s)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4
Spectrum of simulated ectopic signal
Frequency Hz
PS
D
(a) Simulated HRV with Ectopic beats (b) Its spectrum
Figure 3.1 Simulated HRV signal with Ectopic beats and its spectrum
64
Table 3.1 illustrates the effect of ectopic beats on HRV frequency
metrics. The spectral components of HRV signal are computed using AR
model based method, which uses the HRV analysis software developed by
Niskanen et al (2004). The LF and HF powers are measured in normalized
units (n.u) which represent the relative value of each power component in
proportion to the total power minus the power of VLF component.
Normalization tends to minimize the effect of the changes in total power on
the values of LF and HF components.
The increase in ectopic magnitude level and rise in number of
ectopic beats decreases the LF power and increases the HF power and thereby
reduces the LF/HF ratio. The effect is much more pronounced when the
numbers of ectopic beats are more than one as described in Figure 3.2.
Table 3.1 Frequency Metrics for different levels ( ) of ectopic beats
LF HFLF/HF
freq n.pr freq n.pr
† 1.181 0.096 54.2 0.162 45.8
'0.8 1.061 0.096 51.5 0.162 48.5
'0.7 0.986 0.096 49.6 0.162 50.4
'0.6 0.901 0.096 47.4 0.162 52.6
‡0.6 0.673 0.096 40.2 0.164 59.8
0.6 0.618 0.096 38.2 0.164 61.8
† Signal without ectopic beats
' Signals with two ectopy beats at ( =0.8, 0.7 and 0.6)
‡ Signal with three ectopic beat at ( =0.6)
Signal with four ectopic beat at( =0.6)
65
0
10
20
30
40
50
60
70
PSD in
normalized
units
1 2 3 4 5 6
Different levels of ectopy
Frequency Measures
LF
HF
Figure 3.2 Effect of ectopic beats on simulated HRV signal
3.6.2 Performance Comparison of WF and AROF on Simulated
Signals
The simulated ectopic signals are applied to WF and AROF to
remove the noisy beats. The DWT at level five and Daubechies wavelet-1 is
used to obtain the wavelet coefficients. Following hard thresholding iDWT is
applied to the wavelet coefficients to reconstruct the signal. The frequency
metrics of WF and AROF filtered signals are given in Table 3.2 and LF/HF
ratio in Figure 3.3.
Table 3.2 Performance of WF and AROF on simulated ectopic beat signals
Ectopy
levelWF AROF
LF HF LF HF LF/HF
freq n.pr freq n.pr LF/HF freq n.pr freq n.pr
0.8 1.198 0.096 54.5 0.162 45.5 1.216 0.096 54.9 0.164 45.1
0.7 1.202 0.096 54.6 0.162 45.4 1.216 0.096 54.9 0.164 45.1
0.6 1.093 0.096 52.2 0.162 47.8 1.216 0.096 54.9 0.164 45.1
‡0.6 1.094 0.096 52.3 0.162 47.7 1.186 0.096 54.3 0.164 45.7
0.6 0.991 0.096 49.8 0.162 50.2 1.232 0.096 55.2 0.164 44.8
freq: frequency, n.pr: Normalized power.
nil 0.8 0.7 0.6 ‡0.6 *0.6
Different levels of ectopy
66
The performance of WF is better, when the magnitude level of
ectopy is low ( =0.8) and with less (two) number of ectopic beats. But the
performance of WF on real HRV signal is not the same for the same ectopic
level ( =0.8), which is explained in the next section. The performance of WF
degrades for increase in magnitude level of ectopic beats and rise in number
of ectopic beats (three and four). The performance of AROF is consistent for
increase in magnitude level and rise in number of ectopic beats as shown in
Figure 3.3.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
LF/HF ratio
1 2 3 4 5 6
Different levels of Ectopy
LF/HF Ratio
WF
AROF
nil 0.8 0.7 0.6 ‡0.6 *0.6Different levels of Ectopy
Figure 3.3 Performance comparison of WF and AROF on simulated signal
3.6.3 Effect of Ectopic Beats on Real HRV Signals
A real HRV signal (Figure 3.4(a)) with added one ectopic beat at
=0.6 fraction of the previous RR interval is shown in Figure 3.4(b). Presence
of one ectopic beat at =0.6 level, dominates other signal variations and
affects the spectral content of the original signal. The spectrums of the
original and ectopic signals are shown in Figures 3.4(c) and 3.4(d). Presence
of single ectopic beat not only affects the frequency domain measures, it also
increases the amount of nonlinearity in the HRV signal. The spectral energy
67
spreads and introduces ambiguity in the spectral content of the original signal
as given in Table 3.3. A single ectopic beat disrupt the entire spectrum of the
HRV signal.
0 20 40 60 80 1000.9
1
1.1
1.2
1.3
1.4
1.5
HRV signal
Time (s)
RR
In
terv
als
(m
se
c)
0 20 40 60 80 100
0.8
1
1.2
1.4
1.6
1.8
2
HRV signal with Ectopic beat
Time (s)R
R In
terv
als
(m
se
c)
(a) Original Signal (b) Ectopic beat signal
0 0.1 0.2 0.3 0.4 0.50
0.02
0.04
0.06
0.08
0.1
0.12
0.14
X: 0.2285
Y: 0.1205
AR Spectrum
Frequency Hz
PS
D
X: 0.1543
Y: 0.03231
HF
LF
0 0.1 0.2 0.3 0.4 0.50
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
X: 0.06445
Y: 0.01361
AR Spectrum
Frequency Hz
PS
D
X: 0.2383
Y: 0.04345
HF
LF
(c) Spectrum of original signal (d) Spectrum of ectopic signal
Figure 3.4 Original and Ectopic signals and its spectrums
Table 3.3 Spectral components of original and ectopic beat signal
SignalVLF
(Hz)
VLF
power
s2/Hz
LF
(Hz)
LF
power
s2/Hz
HF
(Hz)
HF
power
s2/Hz
Original 0.0451 0.0146 0.1543 0.0323 0.2285 0.1205
Signal with
Ectopy ( =0.6)0.0451 0.0 0.0644 0.0136 0.2383 0.0435
68
3.6.4 Performance of AROF and WF on Real HRV Signal
The performance of AROF and WF on ectopic signal is described
in Figures 3.5(a) to 3.5(h). Ectopic beats activated in the ventricles are fairly
common in subjects suffering from heart failure. Hence to study the
performance of two filters, a congestive heart failure (CHF) signal as
shown in Figure 3.5(a) is considered. The AR spectrum of CHF signal is
shown in Figure 3.5(b).
In original CHF signal, the LF power is much suppressed compared
to VLF and HF powers and the spectral values are given in Table 3.4. Three
ectopic beats at =0.8 magnitudes are randomly added to the CHF signal as
shown in Figure 3.5(c). The AR spectrum of ectopic beats CHF signal (Figure
3.5(d)) is much affected by the presence of ectopic beats. The HF power is
increased and LF power is completely reduced to zero as given in Table 3.4.
The AROF and WF (at various decomposition levels) filtered signals and the
corresponding AR spectrums are shown in Figures 3.5(e) to 3.5(h) and the
components values are given in Table 3.4. The non-parametric (Welch’s
periodogram) spectrum of filtered signals are also given in the Appendix 3 for
comparison.
0 50 100 150 200 2500.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
Ectopic beat free CHF signal
Time (s)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6x 10
-4 Spectrum of CHF signal
Frequency (Hz)
PS
D
(a) Ectopic beat free CHF signal (b) Spectrum of CHF signal
Figure 3.5 (Continued)
69
0 50 100 150 200 2500.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Ectopic beat CHF signal
Time (s)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5x 10
-3 Spectrum of Ectopic signal
Frequency (Hz)
PS
D
(c) Signal with Ectopic beats (d) Spectrum of Ectopic signal
0 50 100 150 200 2500.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
Adaptive Rank order filtered signal
Time (s)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6x 10
-4 Spectrum of AROF signal
Frequency (Hz)
PS
D
(e) AROF filtered signal (f) Spectrum of AROF signal
0 50 100 150 200 2500.95
1
1.05
Wavelet Filtered Signal
Time (s)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6x 10
-4 Spectrum of WF signal
Frequency (Hz)
PS
D
(g) WF signal (h) Spectrum of WF signal
Figure 3.5 Performance analysis of AROF and WF on real CHF signal
70
The AROF almost preserves all the signal variations with less
distortion, whereas the WF is not able to preserve the VLF spectral
component even at level 5. At level 7 (Table 3.4) only it covers all the
components of the original CHF signal.
Table 3.4 Spectral components of Original, Ectopic beat signal, AROF
and WF filtered signals
SignalVLF
(Hz)
VLF
power
s2/Hz
LF
(Hz)
LF
power
s2/Hz
HF
(Hz)
HF
power
s2/Hz
CHF 0.0117 5.6E-4 0.0664 7.5E-5 0.3125 5.0E-4
Signal with
Ectopic beats
=0.8)
0.0156 8.9E-4 0.1445 0.00 0.2773 1.92E-3
AROF signal 0.0156 5.5E-4 0.0667 7.3E-5 0.3105 4.7E-4
WF (S=3) 0.0332 0.00 0.0742 2.0E-5 0.3145 4.8E-4
WF (S=5) 0.0156 0.00 0.0625 2.0E-5 0.3105 5.1E-4
WF (S=7) 0.0156 5.1E-4 0.0605 4.0E-5 0.3145 4.8E-4
0%
20%
40%
60%
80%
100%
Relative
powers of
components
Orig AROF WF(s=3) WF(s=5) WF(s=7)
Comparison of spectral powers
HF
LF
VLF
Figure 3.6 Comparison of spectral powers of Original, AROF and WF
filtered signals
71
Figure 3.6 compares the spectral powers of AROF and WF filtered
signals. The AROF filter not only removes the ectopic beats, it also preserves
the signal characteristics for further analysis. WF filter removes the beats, but
at lower decomposition levels it is not able to preserve the VLF variations of
HRV signals. The increased level of wavelet decomposition may increase the
computational complexity of the algorithm.
3.6.5 Advantage of Adaptive Thresholds in ATROF
The AROF is non-adaptive in its threshold conditions, which may
not track the non-stationary trend of HRV signal. If trends are complex then it
should be detrended prior to processing. The proposed ATROF filter has
adaptable threshold conditions which is able to track the complex trend of
HRV signal. The HRV signal with complex trend is shown in Figure 3.7(a)
and artificially added four ectopic beats are shown in Figure 3.7(b). The
AROF is unable to remove the ectopic beats completely, due to non adaptive
threshold condition for the complex non stationary trend as shown in Figure
3.7(c). The fixed thresholds are able to detect and correct ectopic beat 1
completely, but ectopic beats 2, 3 and 4 are only partly removed. The adaptive
threshold condition of the proposed ATROF tracks the non-stationary trend
and completely removes all the noisy beats as shown in Figure 3.7(d). The
spectral components are given in Table 3.5 for comparison. The comparisons
of spectral values are shown in Figure 3.8.
72
0 50 100 150 200 250 300 3500.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
HRV signal without any noisy beats
Beat Number
RR
In
terv
als
0 50 100 150 200 250 300 3500.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
HRV signal with noisy beats
Beat number
RR
In
terv
als
Ectopic beat 1
Ectopic beat 2
Ectopic beat 3
Ectopic beat 4
(a) HRV with complex trend (b) Signal with Ectopic beats
0 50 100 150 200 250 300 350
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Rank order filtered signal
Beat Number
RR
In
terv
als
Unfiltered noisy
beat
Unfiltered noisy beat
0 50 100 150 200 250 300 3500.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
Adaptive Threshold Rank order filtered signal
Beat Number
RR
In
terv
als
(c) Performance of AROF (d) Performance of ATROF
Figure 3.7 Advantage of adaptive thresholds in ATROF
Table 3.5 Performance comparison of AROF and ATROF
SignalVLF
(Hz)
VLF
power
s2/Hz
LF
(Hz)
LF
power
s2/Hz
HF
(Hz)
HF
power
s2/Hz
Original 0.0312 0.050 0.1445 0.0128 0.2285 0.0294
Signal with
Ectopy( =0.6)0.002 0.0484 0.1362 0.00 0.2226 0.023
AROF 0.0312 0.0392 0.1367 0.0111 0.2305 0.0241
ATROF 0.0312 0.0410 0.1367 0.0119 0.2305 0.0261
73
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Spectral
powers
Original Ectopic AROF ATROF
Performance of AROF and ATROF
VLF
LF
HF
Figure 3.8 Performance comparisons of AROF and ATROF
Figure 3.8 shows the proposed adaptive threshold condition
improves the spectral powers of components by completely removing all the
noisy beats. Hence, it eliminates the need for de-trending prior to ectopic beat
filtering.
3.6.6 Performance Analysis of ATROF and WF on Real Ectopic Beat
Congestive Heart Failure signals
The performance analysis of ATROF on real CHF signal with
varying ectopic beats proves the advantage of ATROF. The ectopic beats in
the CHF signal introduces ambiguity in the VLF and LF bands of HRV
signal. In real situations, the true value of the signal’s PSDs value are
unknown and it is difficult to demonstrate which method yields better results.
Hence, an ectopic free segment has been chosen for reference in the same
signal. The selected ectopic beats segments are of equal length and with rise
in number of ectopic beats. The spectral values of each ectopic beat segment
are given in Table 3.6(a). Application of ATROF on ectopic segments
preserves the VLF component, whereas the WF filter does not preserve the
74
VLF components. The spectral values of ATROF and WF filtered segments
are given in Tables 3.6(b) and 3.6(c). The average spectral values of ATROF
filtered segments are similar to spectral features of ectopic free segment, but
the average LF component spectral values of WF filtered signals are totally
different from ectopic free spectral feature. The WF filter completely
suppresses the VLF variations even at fifth level of wavelet decomposition.
Figures 3.9(a) to 3.9(h) show the performance of ATROF on real ectopic CHF
signal.
0 50 100 150 200 2500.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Ectopic free segment of CHF signal
Time (secs)
RR
in
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6x 10
-4 Spectrum of ectopic free segment
Frequency (Hz)
PS
D
(a) Ectopic beat free segment of (b) its spectrum
CHF signal
0 50 100 150 200 2500.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Real Ectopic beats signal
Time (secs)
RR
In
terv
als
(se
cs
)
0 0.1 0.2 0.3 0.4 0.50
1
2
x 10-4
Spectrum of Congestive heart failure signal
Frequency Hz
PS
D
(c) Ectopic beat CHF signal (d) its spectrum
Figure 3.9 (Continued)
75
0 50 100 150 200 2500.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
ATROF filtered CHF signal
Time (secs)
RR
In
terv
als
(m
se
cs)
0 0.1 0.2 0.3 0.4 0.50
1
2
x 10-4 ATROF filtered CHF signal
Frequency Hz
PS
D
(e) ATROF filtered signal (f) its spectrum
0 50 100 150 200 2500.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Time (secs)
RR
In
terv
als
(m
se
cs)
WF filtered CHF signal
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6
7
8
9x 10
-5 Spectrum of WF filtered CHF signal
Frequency Hz
PS
D
(g) WF filtered signal (h) its spectrum
Figure 3.9 Performance Analysis of ATROF and WF on real ectopic
beat CHF signals
Table 3.6(a) Spectral components of real CHF signal and segments with
ectopic beats
SignalVLF
(Hz)
VLF
power
s2/Hz
LF
(Hz)
LF
power
s2/Hz
HF (Hz)
HF
power
s2/Hz
Ectopic free segment 0.0352 94.5 0.1270 1.0 0.2539 4.5
one ectopic beat 0.0000 0 0.0469 79.7 0.3340 20.3
Two ectopic beat 0.0332 55.6 0.0000 0.0 0.3574 44.4
Three ectopic beat 0.0000 40.1 0.0000 0.0 0.3867 59.9
Four ectopic beat 0.0000 37.1 0.0000 0.0 0.3340 62.9
Five ectopic beat 0.0293 34.6 0.0000 0.0 0.3496 65.4
76
Table 3.6(b) Spectral components of ATROF filtered CHF signals
SignalVLF
(Hz)
VLF
power
s2/Hz
LF (Hz)
LF
power
s2/Hz
HF (Hz)
HF
power
s2/Hz
Ectopic free segment 0.0352 94.5 0.1270 1.0 0.2539 4.5
one ectopic beat 0.0000 0 0.0449 95.9 0.2676 4.1
Two ectopic beat 0.0332 93.2 0.0000 0.0 0.1973 6.8
Three ectopic beat 0.0273 89.9 0.0000 0.0 0.2168 10.1
Four ectopic beat 0.0313 91.0 0.0000 0.0 0.2324 9.0
Five ectopic beat 0.0391 88.3 0.0000 0.0 0.2129 11.7
Average 0.02618 72.48 0.00898 19.18 0.2254 8.34
Table 3.6(c) Spectral components of WF filtered CHF signals
SignalVLF
(Hz)
VLF
power
s2/Hz
LF (Hz)
LF
power
s2/Hz
HF (Hz)
HF
power
s2/Hz
Ectopic free segment 0.0352 94.5 0.1270 1.0 0.2539 4.5
one ectopic beat 0.0000 0 0.0527 79.3 0.1719 4.0
Two ectopic beats 0.0000 0.0 0.0645 82.5 0.2109 17.5
Three ectopic beats 0.0000 0.0 0.0605 72.7 0.2168 27.3
Four ectopic beats 0.0000 0.0 0.0684 64.9 0.1777 35.1
Five ectopic beats 0.0000 0.0 0.0586 75.4 0.2129 24.6
Average 0 0 0.06094 74.96 0.19804 21.7
0102030405060708090
100
Relative power
Ectopic free ATROF WF
Performance Analysis
VLF
LF
HF
Figure 3.10 Average spectral powers of ATROF and WF on real ectopic
segments of CHF signal
77
The Performance comparison of ATROF and WF on real Ectopic
signal shows (Figure 3.10) that ATROF not only removes the noisy beats, it also
preserves the signal characteristics (enhanced VLF variations and suppressed
LF and HF variations) of different ectopic beat segments of CHF signal.
3.6.7 Performance of ATROF and WF on Missed QRS Complex Signal
Missed QRS complexes increase the beat intervals twice the value
of the original beat as shown in Figure 3.11(a). The ATROF filter and WF
filters are applied to remove the missed beats as shown in Figure 3.11(b) and
(c). The VLF power of the missed beat signal is much suppressed by the noisy
impulses. ATROF filtering improves the VLF power in the signal as shown in
Figure 3.12, but WF filtering is not able to preserve the very low frequency
variations of the signal, the spectral components are given in Table 3.7.
0 50 100 150 200 250
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Missed Beats
Beat Numbers
RR
In
terv
als
0 50 100 150 200 2500.65
0.7
0.75
0.8
0.85
0.9
ATROF Signal
Beat Number
RR
In
terv
als
(a) Missed QRS complex signal (b)ATROF filtered signal
0 50 100 150 200 2500.65
0.7
0.75
0.8
0.85
0.9
Wavelet filtered signal
Time (secs)
RR
In
terv
als
(c) Wavelet filtered signal
Figure 3.11 Performance of ATROF and WF on missed QRS complex signal
78
Table 3.7 Performance comparison of ATROF and WF on missed beat
signal
SignalVLF
(Hz)
VLF
power
s2/Hz
LF
(Hz)
LF
power
s2/Hz
HF
(Hz)
HF
power
s2/Hz
Noise free segment 0.0000 32.8 0.0859 53.3 0.2793 13.9
Segment with missed
beats0.0000 2.6 0.0762 48.6 0.1816 48.9
ATROF 0.0000 37.2 0.0977 44.9 0.2852 17.9
WF 0.0000 0.1 0.0488 79.7 0.2090 20.3
0
10
20
30
40
50
60
70
80
Relative power
Noise free Noisy ATROF WF
Performance of ATROF & WF on missed beat signal
VLF
LF
HF
Figure 3.12 Performance comparisons of ATROF and WF on missed
beat signal
3.7 CONCLUSION
Ectopic beats and missed QRS complexes increase the signal HF
power by lowering the LF power and suppressing the VLF power of the
signal. Removal of noisy beats is of prime importance before signal analysis
to avoid ambiguity in the measures. Conventional preprocessing methods
assume functional forms (wavelet functions) which are not adaptive to the
79
complexity of HRV signal. Non-stationary is the characteristic feature of
HRV signal, and conventional methods assume linear and weak stationary
conditions in the HRV signal. The proposed ATROF method does not assume
any functional forms or linear, stationary conditions in the HRV signal. The
adaptive window size, adaptive filtering and adaptive threshold conditions
make the filter completely automatic and adaptive to the signal complexity.
Application of ATROF even at 30% of noisy beats affects only the high
frequency details and the structural complexity of the signal is preserved as
shown in Figure 3.13.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.01
0.02
0.03
0.04
0.05
0.06
Frequency (Hz)
PS
D
Performance Analysis of ATROF
Original HRV signal
5% noise removed
20% noise removed
30% noise removed
Figure 3.13 Performance analysis of ATROF on PSD of HRV signal
The proposed ATROF is completely adaptive and preserves the
signal characteristics for further analysis.