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Noninvasive fetal ECG estimation using adaptive comb filter
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Noninvasive fetal ECG estimation using adaptive comb filter夽 Zheng Wei a,∗ , Wei Xueyun a , Zhong Jian jian b , Liu Hongxing c a b c
School of Electronic Information, Jiangsu University of Science and Technology, ZhenJiang, China Obstetrics and Gynecology Department, The Fourth People’s Hospital of Zhenjiang, ZhenJiang, China School of Electronic Science and Engineering, Nanjing University, Nanjing, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper describes a robust and simple algorithm for fetal electrocardiogram (FECG) esti-
Received 16 October 2012
mation from abdominal signal using adaptive comb filter (ACF). The ACF can adjust itself
Received in revised form 6 June 2013
to the temporal variations in fundamental frequency, which makes it qualified for the esti-
Accepted 21 July 2013
mation of quasi-periodic component from physiologic signal, such as ECG. The validity and
Keywords:
data. A comparison with the well-known independent component analysis (ICA) method
Adaptive comb filter
has also been presented.
performance of the described method are confirmed through experiments on real fetal ECG
Fetal electrocardiogram estimation
© 2013 Elsevier Ireland Ltd. All rights reserved.
Quasi-periodic physiologic signal
1.
Introduction
Estimation of the fetal electrocardiogram (FECG) to evaluate the health and condition of the fetus is a classical problem in biomedical engineering, that remains a challenging issue. Various techniques have been employed to estimate the FECG from the abdominal ECG signal of the pregnant woman, including adaptive filtering [1,2], blind source separation (BSS) [3–5], neural network [6], and comb filter [7]. A comb filter can be used to extract a periodic signal that is buried in noise, provided the teeth of the comb coincide with the harmonics of the periodic signal. One of the key challenges in applying a comb filter to quasi-periodic physiologic signals, such as ECG, is that the fundamental frequency is
often nonstationary and varies substantially among subjects. In our previous work, a comb filter has been made feasible to estimate FECG by resampling each R–R interval [7]. To filter noise corrupted harmonic signals whose parameters are time varying, it is desirable to apply adaptive filtering. Most existing adaptive filters do not account for the special structure of the harmonic spectrum, thus, their performance is not likely to be optimal for such signals [8]. In this paper, we introduce the adaptive comb filter (ACF) to estimate the FECG from the abdominal ECG signal. Although many investigators have applied ACF to speech signal [9,10], relatively little has been reported on application to physiologic signal. The ACF can adjust itself to the temporal variations in fundamental frequency, and it can be designed to estimate harmonic signals measured with broad-band process.
Abbreviations: FECG, fetal electrocardiogram; MECG, maternal ECG; EMG, electromyogram; ACF, adaptive comb filter; BSS, blind source separation; SNR, signal to noise ratio; ICA, independent component analysis. 夽 This work was supported by National Science Foundation of China under Grant 61271079. ∗ Corresponding author. Tel.: +86 051184401015; fax: +86 051184427900. E-mail address: [email protected] (Z. Wei). 0169-2607/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cmpb.2013.07.015
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
2.
Methods
2.1.
Adaptive comb filter
An adaptive comb filtering operation, which adjusts itself to the temporal variations in fundamental frequency, passes only the harmonics of the signal, and filters out spectral components in the frequency region between harmonics. Since detailed explanation associated ACF can be found in [9,10], only a brief description is given in this section. The operation of an adaptive comb filtering can be explained by considering its unit sample response over one period:
h(n) =
L
ak ı(n − Nk )
(1)
k=−L
Here, h(n) is the unit sample response, ı(n) is unit sample function, the length of the filter is 2L + 1 period, ak is the filter L coefficient that satisfies a = 1, and Nk is given by the k=−L k following equations:
Nk =
⎪ ⎪ k−1 ⎪ ⎪ ⎪ ⎪ Tl , ⎪ ⎩
k=0
(2)
k>0
l=0
where Tl corresponds to the particular period which contains the points of waveform that is multiplied by the filter coefficient ak . The ACF represented in Eq. (2) is a noncausal filter version, a minus sign in the case k < 0 make the h(n) use the “future inputs”. It is applicated to the block data (off-line mode) in our work. An example of ACF operation in one period block of an ECG signal with L = 2 has been shown in Fig. 1. The filter coefficients are unchanged and only Nk is updated once every period based on fundamental frequency information of the waveform being processed. Its unit sample response h(n) is not fixed, the frequency response of the filter would change over time. This adaptation amounts to aligning the “teeth” of the comb filter to the harmonics of quasi-periodic component once every period without changing the overall filter response characteristics.
2.2.
ak =
0.54 + 0.46 cos(k/L)
L
for − L ≤ k ≤ L
(3)
0.54 + 0.46 cos(k/L)
K=−L
⎧ −1 ⎪ ⎪ ⎪ − Tl , k < 0 ⎪ ⎪ ⎪ ⎪ ⎨ l=k 0,
due to the heart rate variability, thus the lengths of every RR interval are different. The ACF algorithm is implemented in period block, and the parameter Nk of the ACF is updated once every period block. The period block is composed of the two half cycle of the adjacent R–R intervals, instead of one whole R–R interval. This is in order to avoid the “overload problem” / 0), more detailed descripwhen T0 is longer than any of Ti (i = tion of “overload problem” in ACF can be found in [11]. The filter coefficients ak which determine the unit sample response of the ACF h(n) were chosen from different shapes corresponding to Hamming, Hanning, and Blackman windows. The basic principles to choses the coefficients ak is that the weights of the filter decrease from the center to both sides. There was little difference in performance by the Hamming, Hanning, and Blackman windows. The ACF filter used in this paper adopts a Hamming window shape which is obtained from the following equation:
The described ACF algorithm could serve both in MECG estimation stage and FECG enhancement stage according to fundamental frequency of MECG and FECG respectively. Thus the maternal R-wave peaks in the abdominal signal and the fetal R-wave peaks in the residual signal should been detected in advanced. In this paper, the R-peaks detection algorithm is developed through a combination of earlier techniques [12,13]. The ECG signal is first passed through a finite impulse response bandpass filter (cut-off frequencies of 10 and 40 Hz) using a Hamming window. The digital filter’s coefficients have been chosen to effectively pass the highest power density of the maternal and fetal R waves. The next routine detects the time and magnitude of local maxima and minima of the waveform. The absolute value of the difference between successive peaks and valleys is computed for each max-to-min or minto-max interval. A single sample value equal to this difference is output at the midpoint of each interval, while the remaining discrete time output points in the interval are set to 0. At last, two medical rules were applied to include or reject a candidate R-peak [14]. This set of operations is used to detect the maternal R-peaks in abdominal signal and fetal R-peaks in residual signal respectively.
Adaptive comb filter for FECG estimation
The FECG estimation algorithm using ACF is composed of two cascaded parts. The first estimates the maternal ECG (MECG) component in the abdominal signal and subtracts it, and the second enhances the FECG in the residual signal. The two sets of operations in this two-fold filtering problem are both based on ACF with the fundamental frequency of MECG and FECG respectively. It is worthwhile to note that the estimation algorithm needs only one abdominal ECG signal, which is more convenient in real application. Fig. 1 describes a simple ACF operation in one period block when setting L = 2. The period of the ECG signal is time-varied
3.
Results
To investigate the effectiveness of the described method for FECG estimation from the abdominal ECG signal, it has been applied to the DaISy fetal ECG data [15] and Non-Invasive Fetal Electrocardiogram Database from PhysioNet [16]. To further assess and validate the described method, a comparison has been made with the well-known independent component analysis (ICA) methods. A fast fixed-point algorithm for ICA described in [17] is applied to the same data.
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
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Fig. 1 – Example of an adaptive comb filter in one period block of an ECG signal with L = 2.
3.1.
DaISy fetal ECG data
The DaISy fetal ECG data consists of five abdominal and three thoracic channels recorded from the abdomen and chest of a pregnant woman with a sampling rate of 250 Hz, showing in Fig. 2. This data is very popular for FECG
estimation method validation in many related literatures. The signal to noise ratio (SNR) of the data is relatively high, and the fetal ECG component is visible in the abdominal signal. The noise in the abdominal signal is generally smooth, thus it is not very difficult to estimate the FECG from this data.
Fig. 2 – DaISy fetal ECG data (10 s). Ch1–Ch5: abdominal signals, Ch6–Ch8: thoracic signals.
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
Fig. 3 – FECG estimation by ACF using Ch1–Ch3 abdominal signals in Fig. 2.
The described method needs only one abdominal ECG signal for FECG estimation. The ACF based method is applied to the Ch1–Ch3 abdominal signals one by one, and the result is shown in Fig. 3. It can be found that the FECG has been
estimated from the abdominal signal successfully. The parameter L of the unit sample response of ACF h(n) has been set to be 2 in experiments. Increasing the value of L is not recommended only when the noise is very strong, because the higher
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
129
Fig. 4 – FECG estimation by ACF step by step using Ch5 abdominal signals in Fig. 2.
order of the ACF may lead to lose the local characteristic of the FECG. Fig. 4 shows the frequency imformation of the ECG signals in each stage of the ACF processing using Ch5 abdominal signals in Fig. 2, which give the frequency characteristic of the adaptive comb filter. For comparison, Hyvarinen’s fast fixed-point algorithm for ICA described in [17] is applied to the Ch1–Ch8 signals in Fig. 2, and the result is shown in Fig. 5. IC1 and IC5 signals are obvious the estimated FECG components. The interesting thing is that although the two kinds of fatal ECG estimated by ACF and ICA respectively are different, both of them can be considered as the reasonable estimates based on respective theoretical model. The ACF estimates surface FECG signal, which is very straightforward, and the ICA estimates source fetal ECG signal which can be interpreted as the coordinates of the fetal heart dipole. It is very probable that the fetal and maternal ECG overlap, and it had happened to the DaISy fetal ECG data. Although the maternal and fetal ECG overlap in the time and frequency domain, it is possible to separate them by adptive comb filter, which is a nolinear process as a whole. The overlap segments have been denoted in Figs. 3 and 5, and it is shown that the ACF/ICA method could recover the fetal component successfully. The total execution time of our proposed method (including R-peak detection, adaptive comb filter) to estimate fetal ECG signal is approximately 0.25 s. The execution time of fast fixed-point algorithm for ICA is approximately 0.53 s. Matlab codes are carried on a general PC, 2.5 GHz Dual Core Processor.
3.2.
PhysioNet fetal ECG data
The PhysioNet database contains a series of 55 multi-channel abdominal fetal ECG recordings, taken from a single subject between 21 to 40 weeks of pregnancy with varying SNR. Every recording includes 2 thoracic signals and 3 or 4 abdominal signals, and the durations of the signals are between 144 s and 2780 s. A 1-kHz sampling frequency and 16-bit resolution were employed. Fig. 6 is a segment of the “ecgca445” signal recording at 22 gestational weeks plus 1 day. Ch1–Ch2 are thoracic signals, and Ch3–Ch5 are abdominal signals. The non-stationary noise, such as electromyogram (EMG) by uterine contraction, are very strong in these abdominal signals. The SNR of the data is relatively lower than the DaISy fetal ECG data. These records have proven to be useful for testing signal separation algorithms. For comparison, Hyvarinen’s fast fixed-point algorithm for ICA is also applied to the Ch1–Ch5 signals in Fig. 6, and the result is shown in Fig. 7. IC1–IC2 signals are obvious the MECG components, but it is hardly to find the FECG in IC3–IC5 signals. Five input mixed signals are probably not enough for the ICA method. The number of estimated sources is confined to the dimension of the input mixture, so that different dimensions of the input mixture may bring out different results of estimated sources. A lower dimension of input mixture may prohibit the algorithm from extracting the FECG. The lower SNR of the data may be another reason of fail. In the same way, the ACF has also applied to the Ch3–Ch5 abdominal signals in Fig. 6 one by one, and the result is shown
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
Fig. 5 – FECG estimation by ICA method using Ch1–Ch8 signals in Fig. 2.
Fig. 6 – A segment (5 s) of the “ecgca445” signal recording at 22 gestational weeks plus 1 day. Ch1–Ch2: thoracic signals, Ch3–Ch5: abdominal signals.
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
Fig. 7 – FECG estimation by ICA method using Ch1–Ch5 signals in Fig. 6.
in Fig. 8. Although the background noise is very strong, the FECG signals are still estimated clearly, and the parameters of ACF are not changed, which has demonstrated the robustness of the algorithm. Fig. 9 shows the frequency imformation of the ECG signals in each stage of the ACF processing using “ecgca826” signal recording in PhysioNet. In order to validate the performance of the proposed method in varying SNR, The PhysioNet dataset with all its sample data have been used to validate the proposed method, and the result is shown in Table 1. According to the current technical level in the area of fetal ECG processing, the authors suggest that the reasonable estimates of FECG should meet the following two requirements: the maternal ECG component has been eliminated, and the fetal characteristic waves (QRS complexes at least) should stand out in the final outcome waveform. In the resulte of Table 1, the proposed method can obtain reasonable estimates of the FECG for approximately 60% of the abdominal signals in this database. Moreover, the authors find that the result has a close relationship with
gestational weeks, relatively high success rate at 22–25 and 35–40 gestational weeks.
4. Discussion on fetal R-peak detection errors The fetal R-peak detection is a critical stage in our methodology, which directly influences the performance of this method. When the fetal components are very weak, or the background noise is strong, the fetal R-peak detection errors often happen to the residual ECG signals after removal of the maternal ECG components. The authors have observed the recordings with FECG estimation failure in the PhysioNet fetal ECG database and could not find repeating fetal QRS complexes in the abdominal waveforms by the naked eye. The fetal R-peaks in the corresponding residual signals are too weak to be detected, resulting in the failure of fetal ECG estimation. A failure example for a low SNR signal due to the fetal R-peak detection
Table 1 – Evaluation of ACF using the fetal ECG database from the PhysioNet. Recording (week + day)
Recording (week + day)
Recording (week + day)
Recording (week + day)
Recording (week + day)
ecgca102 (22 + 1)a ecgca154 (22 + 1)a ecgca192 (22 + 1)a ecgca445 (22 + 1)a ecgca748 (22 + 1)a ecgca811 (22 + 1)a ecgca876 (22 + 1)a ecgca900 (22 + 1)b ecgca274 (23 + 6)a ecgca300 (23 + 6)a ecgca649 (23 + 6)a
ecgca323 (23 + 6)a ecgca902 (23 + 6)b ecgca986 (23 + 6)a ecgca997 (23 + 6)b ecgca848 (24 + 2)a ecgca368 (24 + 2)a ecgca410 (24 + 2)a ecgca826 (24 + 2)a ecgca571 (25 + 0)a ecgca880 (25 + 0)b ecgca115 (27 + 6)b
ecgca252 (29 + 2)b ecgca816 (29 + 2)b ecgca308 (30 + 5)b ecgca621 (30 + 5)b ecgca864 (30 + 5)b ecgca127 (31 + 4)b ecgca384 (31 + 4)a ecgca436 (31 + 4)b ecgca699 (32 + 3)b ecgca868 (32 + 3)b ecgca998 (32 + 3)b
ecgca392 (33 + 4)a ecgca416 (33 + 4)b ecgca776 (33 + 4)b ecgca968 (33 + 4)b ecgca896 (34 + 6)b ecgca595 (35 + 6)a ecgca629 (35 + 6)a ecgca659 (35 + 6)a ecgca515 (37 + 1)b ecgca711 (37 + 1)b ecgca244 (38 + 0)a
ecgca290 (38 + 0)a ecgca733 (38 + 0)a ecgca585 (38 + 2)a ecgca597 (38 + 2)a ecgca886 (38 + 2)a ecgca444 (39 + 0)a ecgca840 (39 + 0)a ecgca746 (39 + 6)a ecgca771 (39 + 6)b ecgca473 (40 + 2)a ecgca906 (40 + 2)a
a b
A reasonable estimation. A failing estimation.
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
Fig. 8 – FECG estimation by ACF using Ch3–Ch5 abdominal signals in Fig. 5.
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
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Fig. 9 – FECG estimation by ACF step by step using “ecgca826” signal recording at 24 gestational weeks plus 2 day.
Fig. 10 – A failure example for a low SNR signal “ecgca115” due to the fetal R-peak detection errors.
errors has been shown in the Fig. 10. Multiple channels fusion could be considered as a good solution for improving the R peaks detection. The authors would plan to detect the R peaks using multiple abdominal ECG signals in next research stage.
5.
Conclusion
The difference between the FECG and normal noise in abdominal signal is that the FECG is quasi-periodic, and the fundamental frequency of MECG and FECG is different.
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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
Therefore, the adaptive comb filter is suited to estimate the FECG form abdominal signal. The described algorithm is simple and robust, without limitations of the any particular recording technique. The single-lead feature is desirable from the comfort point of view of the patient especially during longterm monitoring.
Conflict of interest We declare that we do not have conflicts of interest.
Appendix A. Pseudo-code of the proposed method 1. 2.
load the abdominal ECG signals a(n) preprocessing 0.05–100 Hz band-pass FIR filter;
3. 4.
removing 50 Hz/60 Hz power line interference; detect the maternal R peaks in a(n); determine the unit sample response hm (n) of ACF for maternal ECG estimation: hm (n) =
Nk =
L
ak ı(n − Nk )
⎧ k=−L −1 ⎪ ⎪ ⎪ − Tl , k < 0 ⎪ ⎪ ⎪ ⎨ l=k 0,
⎪ k−1 ⎪ ⎪ ⎪ ⎪ Tl , ⎪ ⎩
k=0 k>0
l=0
maternal ECG estimation from a(n): mecg(n) = convolution (a(n), hm (n)); 6. obtain the residual ECG signal by r(n) = a(n) − mecg(n); 7. detect the fetal R peaks in r(n); 8. determine the unit sample response hf (n) of ACF for fetal ECG estimation: 9. fetal ECG estimation from r(n): fecg(n) = convolution (r(n), hf (n)); 10. end
5.
references
[1] B. Widrow, J.R. Glover, J.M. McCool, J. Kaunitz, C.S. Williams, R.H. Hearn, J.R. Zeidler, E. Dong, R.C. Goodlin, Adaptive noise cancelling: principles and applications, Proceedings of the IEEE 63 (12) (1975) 1692–1716.
[2] Z. Wei, L. Hongxing, C. Jianchun, Adaptive filtering in phase space for foetal electrocardiogram estimation from an abdominal electro-cardiogram signal and a thoracic electrocardiogram signal, IET Signal Processing 6 (3) (2012) 171–177. [3] L. De Lathauwer, B. De Moor, J. Vandewalle, Fetal electrocardiogram extraction by blind source subspace separation, IEEE Transactions on Biomedical Engineering 47 (May (5)) (2000) 567–572. [4] R. Sameni, Multichannel electrocardiogram decomposition using periodic component analysis, IEEE Transactions on Biomedical Engineering 55 (8) (2008) 1935–1940. [5] R. Martın-Clemente, J.L. Camargo-Olivares, S. Hornillo-Mellado, M. Elena, I. Roman, Fast technique for noninvasive fetal ECG extraction, IEEE Transactions on Biomedical Engineering 58 (February (2)) (2011) 227–230. [6] K. Assaleh, Extraction of fetal electrocardiogram using adaptive neuro-fuzzy inference systems, IEEE Transactions on Biomedical Engineering 54 (June (1)) (2007) 59–68. [7] Z. Wei, L. Hongxing, H. Aijun, N. Xinbao, C. Jianchun, Single-lead fetal electrocardiogram estimation by means of combining R-peak detection, resampling and comb filter, Medical Engineering & Physics 32 (7) (2010) 708–719. [8] A. Nehorai, B. Porat, Adaptive comb filtering for harmonic signal enhancement, IEEE Transactions on Acoustics Speech and Signal Processing ASSP-34 (October) (1986) 1124–1138. [9] R.H. Frazier, S. Samsam, L.D. Braida, A.V. Oppenheim, Enhancement of speech by adaptive filtering, in: Proc. IEEE Int. Conf. on Acoust., Speech, and Signal Processing, Philadelphia, PA, API. 12–14, 1976, pp. 251–253. [10] J.S. Lim, A.V. Oppenheim, L.D. Braida, Evaluation of an adaptive comb filtering method for enhancing speech degraded by white noise addition, IEEE Transactions on Acoustics Speech and Signal Processing ASSP-26 (August) (1978) 354–358. [11] R.H. Frazier, An adaptive filtering approach toward speech enhancement, MIT, Cambridge, 1975 (S.M. thesis). [12] S. Azevedo, R.L. Longini, Abdominal-lead fetal electrocardiographic R-wave enhancement for heart rate determination, IEEE Transactions on Biomedical Engineering 27 (5) (1980) 255–260. [13] M.I. Ibrahimy, F. Ahmed, M.A. Mohd Ali, E. Zahedi, Real-time signal processing for fetal heart rate monitoring, IEEE Transactions on Biomedical Engineering 50 (2) (2003) 258–262. [14] S. Abboud, A. Beker, An improved detection algorithm in fetal electrocardiography, Journal of Electrocardiology 22 (Suppl.) (1989) 238–242. [15] B. De Moor, Database for the Identification of Systems (DaISy) [Online]. Available at: http://homes.esat.kuleuven.be/∼smc/daisy/ [16] The MIT-BIH Non-Invasive Fetal Electrocardiogram Database [Online]. Available at: http://www.physionet.org/pn3/nifecgdb [17] A. Hyvarinen, E. Oja, A fast fixed-point algorithm for independent component analysis, Neural Computation 9 (7) (1997) 1483–1492.
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Noninvasive fetal ECG estimation using adaptive comb filter夽 Zheng Wei a,∗ , Wei Xueyun a , Zhong Jian jian b , Liu Hongxing c a b c
School of Electronic Information, Jiangsu University of Science and Technology, ZhenJiang, China Obstetrics and Gynecology Department, The Fourth People’s Hospital of Zhenjiang, ZhenJiang, China School of Electronic Science and Engineering, Nanjing University, Nanjing, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper describes a robust and simple algorithm for fetal electrocardiogram (FECG) esti-
Received 16 October 2012
mation from abdominal signal using adaptive comb filter (ACF). The ACF can adjust itself
Received in revised form 6 June 2013
to the temporal variations in fundamental frequency, which makes it qualified for the esti-
Accepted 21 July 2013
mation of quasi-periodic component from physiologic signal, such as ECG. The validity and
Keywords:
data. A comparison with the well-known independent component analysis (ICA) method
Adaptive comb filter
has also been presented.
performance of the described method are confirmed through experiments on real fetal ECG
Fetal electrocardiogram estimation
© 2013 Elsevier Ireland Ltd. All rights reserved.
Quasi-periodic physiologic signal
1.
Introduction
Estimation of the fetal electrocardiogram (FECG) to evaluate the health and condition of the fetus is a classical problem in biomedical engineering, that remains a challenging issue. Various techniques have been employed to estimate the FECG from the abdominal ECG signal of the pregnant woman, including adaptive filtering [1,2], blind source separation (BSS) [3–5], neural network [6], and comb filter [7]. A comb filter can be used to extract a periodic signal that is buried in noise, provided the teeth of the comb coincide with the harmonics of the periodic signal. One of the key challenges in applying a comb filter to quasi-periodic physiologic signals, such as ECG, is that the fundamental frequency is
often nonstationary and varies substantially among subjects. In our previous work, a comb filter has been made feasible to estimate FECG by resampling each R–R interval [7]. To filter noise corrupted harmonic signals whose parameters are time varying, it is desirable to apply adaptive filtering. Most existing adaptive filters do not account for the special structure of the harmonic spectrum, thus, their performance is not likely to be optimal for such signals [8]. In this paper, we introduce the adaptive comb filter (ACF) to estimate the FECG from the abdominal ECG signal. Although many investigators have applied ACF to speech signal [9,10], relatively little has been reported on application to physiologic signal. The ACF can adjust itself to the temporal variations in fundamental frequency, and it can be designed to estimate harmonic signals measured with broad-band process.
Abbreviations: FECG, fetal electrocardiogram; MECG, maternal ECG; EMG, electromyogram; ACF, adaptive comb filter; BSS, blind source separation; SNR, signal to noise ratio; ICA, independent component analysis. 夽 This work was supported by National Science Foundation of China under Grant 61271079. ∗ Corresponding author. Tel.: +86 051184401015; fax: +86 051184427900. E-mail address: [email protected] (Z. Wei). 0169-2607/$ – see front matter © 2013 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cmpb.2013.07.015
126
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 1 2 ( 2 0 1 3 ) 125–134
2.
Methods
2.1.
Adaptive comb filter
An adaptive comb filtering operation, which adjusts itself to the temporal variations in fundamental frequency, passes only the harmonics of the signal, and filters out spectral components in the frequency region between harmonics. Since detailed explanation associated ACF can be found in [9,10], only a brief description is given in this section. The operation of an adaptive comb filtering can be explained by considering its unit sample response over one period:
h(n) =
L
ak ı(n − Nk )
(1)
k=−L
Here, h(n) is the unit sample response, ı(n) is unit sample function, the length of the filter is 2L + 1 period, ak is the filter L coefficient that satisfies a = 1, and Nk is given by the k=−L k following equations:
Nk =
⎪ ⎪ k−1 ⎪ ⎪ ⎪ ⎪ Tl , ⎪ ⎩
k=0
(2)
k>0
l=0
where Tl corresponds to the particular period which contains the points of waveform that is multiplied by the filter coefficient ak . The ACF represented in Eq. (2) is a noncausal filter version, a minus sign in the case k < 0 make the h(n) use the “future inputs”. It is applicated to the block data (off-line mode) in our work. An example of ACF operation in one period block of an ECG signal with L = 2 has been shown in Fig. 1. The filter coefficients are unchanged and only Nk is updated once every period based on fundamental frequency information of the waveform being processed. Its unit sample response h(n) is not fixed, the frequency response of the filter would change over time. This adaptation amounts to aligning the “teeth” of the comb filter to the harmonics of quasi-periodic component once every period without changing the overall filter response characteristics.
2.2.
ak =
0.54 + 0.46 cos(k/L)
L
for − L ≤ k ≤ L
(3)
0.54 + 0.46 cos(k/L)
K=−L
⎧ −1 ⎪ ⎪ ⎪ − Tl , k < 0 ⎪ ⎪ ⎪ ⎪ ⎨ l=k 0,
due to the heart rate variability, thus the lengths of every RR interval are different. The ACF algorithm is implemented in period block, and the parameter Nk of the ACF is updated once every period block. The period block is composed of the two half cycle of the adjacent R–R intervals, instead of one whole R–R interval. This is in order to avoid the “overload problem” / 0), more detailed descripwhen T0 is longer than any of Ti (i = tion of “overload problem” in ACF can be found in [11]. The filter coefficients ak which determine the unit sample response of the ACF h(n) were chosen from different shapes corresponding to Hamming, Hanning, and Blackman windows. The basic principles to choses the coefficients ak is that the weights of the filter decrease from the center to both sides. There was little difference in performance by the Hamming, Hanning, and Blackman windows. The ACF filter used in this paper adopts a Hamming window shape which is obtained from the following equation:
The described ACF algorithm could serve both in MECG estimation stage and FECG enhancement stage according to fundamental frequency of MECG and FECG respectively. Thus the maternal R-wave peaks in the abdominal signal and the fetal R-wave peaks in the residual signal should been detected in advanced. In this paper, the R-peaks detection algorithm is developed through a combination of earlier techniques [12,13]. The ECG signal is first passed through a finite impulse response bandpass filter (cut-off frequencies of 10 and 40 Hz) using a Hamming window. The digital filter’s coefficients have been chosen to effectively pass the highest power density of the maternal and fetal R waves. The next routine detects the time and magnitude of local maxima and minima of the waveform. The absolute value of the difference between successive peaks and valleys is computed for each max-to-min or minto-max interval. A single sample value equal to this difference is output at the midpoint of each interval, while the remaining discrete time output points in the interval are set to 0. At last, two medical rules were applied to include or reject a candidate R-peak [14]. This set of operations is used to detect the maternal R-peaks in abdominal signal and fetal R-peaks in residual signal respectively.
Adaptive comb filter for FECG estimation
The FECG estimation algorithm using ACF is composed of two cascaded parts. The first estimates the maternal ECG (MECG) component in the abdominal signal and subtracts it, and the second enhances the FECG in the residual signal. The two sets of operations in this two-fold filtering problem are both based on ACF with the fundamental frequency of MECG and FECG respectively. It is worthwhile to note that the estimation algorithm needs only one abdominal ECG signal, which is more convenient in real application. Fig. 1 describes a simple ACF operation in one period block when setting L = 2. The period of the ECG signal is time-varied
3.
Results
To investigate the effectiveness of the described method for FECG estimation from the abdominal ECG signal, it has been applied to the DaISy fetal ECG data [15] and Non-Invasive Fetal Electrocardiogram Database from PhysioNet [16]. To further assess and validate the described method, a comparison has been made with the well-known independent component analysis (ICA) methods. A fast fixed-point algorithm for ICA described in [17] is applied to the same data.
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Fig. 1 – Example of an adaptive comb filter in one period block of an ECG signal with L = 2.
3.1.
DaISy fetal ECG data
The DaISy fetal ECG data consists of five abdominal and three thoracic channels recorded from the abdomen and chest of a pregnant woman with a sampling rate of 250 Hz, showing in Fig. 2. This data is very popular for FECG
estimation method validation in many related literatures. The signal to noise ratio (SNR) of the data is relatively high, and the fetal ECG component is visible in the abdominal signal. The noise in the abdominal signal is generally smooth, thus it is not very difficult to estimate the FECG from this data.
Fig. 2 – DaISy fetal ECG data (10 s). Ch1–Ch5: abdominal signals, Ch6–Ch8: thoracic signals.
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Fig. 3 – FECG estimation by ACF using Ch1–Ch3 abdominal signals in Fig. 2.
The described method needs only one abdominal ECG signal for FECG estimation. The ACF based method is applied to the Ch1–Ch3 abdominal signals one by one, and the result is shown in Fig. 3. It can be found that the FECG has been
estimated from the abdominal signal successfully. The parameter L of the unit sample response of ACF h(n) has been set to be 2 in experiments. Increasing the value of L is not recommended only when the noise is very strong, because the higher
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Fig. 4 – FECG estimation by ACF step by step using Ch5 abdominal signals in Fig. 2.
order of the ACF may lead to lose the local characteristic of the FECG. Fig. 4 shows the frequency imformation of the ECG signals in each stage of the ACF processing using Ch5 abdominal signals in Fig. 2, which give the frequency characteristic of the adaptive comb filter. For comparison, Hyvarinen’s fast fixed-point algorithm for ICA described in [17] is applied to the Ch1–Ch8 signals in Fig. 2, and the result is shown in Fig. 5. IC1 and IC5 signals are obvious the estimated FECG components. The interesting thing is that although the two kinds of fatal ECG estimated by ACF and ICA respectively are different, both of them can be considered as the reasonable estimates based on respective theoretical model. The ACF estimates surface FECG signal, which is very straightforward, and the ICA estimates source fetal ECG signal which can be interpreted as the coordinates of the fetal heart dipole. It is very probable that the fetal and maternal ECG overlap, and it had happened to the DaISy fetal ECG data. Although the maternal and fetal ECG overlap in the time and frequency domain, it is possible to separate them by adptive comb filter, which is a nolinear process as a whole. The overlap segments have been denoted in Figs. 3 and 5, and it is shown that the ACF/ICA method could recover the fetal component successfully. The total execution time of our proposed method (including R-peak detection, adaptive comb filter) to estimate fetal ECG signal is approximately 0.25 s. The execution time of fast fixed-point algorithm for ICA is approximately 0.53 s. Matlab codes are carried on a general PC, 2.5 GHz Dual Core Processor.
3.2.
PhysioNet fetal ECG data
The PhysioNet database contains a series of 55 multi-channel abdominal fetal ECG recordings, taken from a single subject between 21 to 40 weeks of pregnancy with varying SNR. Every recording includes 2 thoracic signals and 3 or 4 abdominal signals, and the durations of the signals are between 144 s and 2780 s. A 1-kHz sampling frequency and 16-bit resolution were employed. Fig. 6 is a segment of the “ecgca445” signal recording at 22 gestational weeks plus 1 day. Ch1–Ch2 are thoracic signals, and Ch3–Ch5 are abdominal signals. The non-stationary noise, such as electromyogram (EMG) by uterine contraction, are very strong in these abdominal signals. The SNR of the data is relatively lower than the DaISy fetal ECG data. These records have proven to be useful for testing signal separation algorithms. For comparison, Hyvarinen’s fast fixed-point algorithm for ICA is also applied to the Ch1–Ch5 signals in Fig. 6, and the result is shown in Fig. 7. IC1–IC2 signals are obvious the MECG components, but it is hardly to find the FECG in IC3–IC5 signals. Five input mixed signals are probably not enough for the ICA method. The number of estimated sources is confined to the dimension of the input mixture, so that different dimensions of the input mixture may bring out different results of estimated sources. A lower dimension of input mixture may prohibit the algorithm from extracting the FECG. The lower SNR of the data may be another reason of fail. In the same way, the ACF has also applied to the Ch3–Ch5 abdominal signals in Fig. 6 one by one, and the result is shown
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Fig. 5 – FECG estimation by ICA method using Ch1–Ch8 signals in Fig. 2.
Fig. 6 – A segment (5 s) of the “ecgca445” signal recording at 22 gestational weeks plus 1 day. Ch1–Ch2: thoracic signals, Ch3–Ch5: abdominal signals.
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Fig. 7 – FECG estimation by ICA method using Ch1–Ch5 signals in Fig. 6.
in Fig. 8. Although the background noise is very strong, the FECG signals are still estimated clearly, and the parameters of ACF are not changed, which has demonstrated the robustness of the algorithm. Fig. 9 shows the frequency imformation of the ECG signals in each stage of the ACF processing using “ecgca826” signal recording in PhysioNet. In order to validate the performance of the proposed method in varying SNR, The PhysioNet dataset with all its sample data have been used to validate the proposed method, and the result is shown in Table 1. According to the current technical level in the area of fetal ECG processing, the authors suggest that the reasonable estimates of FECG should meet the following two requirements: the maternal ECG component has been eliminated, and the fetal characteristic waves (QRS complexes at least) should stand out in the final outcome waveform. In the resulte of Table 1, the proposed method can obtain reasonable estimates of the FECG for approximately 60% of the abdominal signals in this database. Moreover, the authors find that the result has a close relationship with
gestational weeks, relatively high success rate at 22–25 and 35–40 gestational weeks.
4. Discussion on fetal R-peak detection errors The fetal R-peak detection is a critical stage in our methodology, which directly influences the performance of this method. When the fetal components are very weak, or the background noise is strong, the fetal R-peak detection errors often happen to the residual ECG signals after removal of the maternal ECG components. The authors have observed the recordings with FECG estimation failure in the PhysioNet fetal ECG database and could not find repeating fetal QRS complexes in the abdominal waveforms by the naked eye. The fetal R-peaks in the corresponding residual signals are too weak to be detected, resulting in the failure of fetal ECG estimation. A failure example for a low SNR signal due to the fetal R-peak detection
Table 1 – Evaluation of ACF using the fetal ECG database from the PhysioNet. Recording (week + day)
Recording (week + day)
Recording (week + day)
Recording (week + day)
Recording (week + day)
ecgca102 (22 + 1)a ecgca154 (22 + 1)a ecgca192 (22 + 1)a ecgca445 (22 + 1)a ecgca748 (22 + 1)a ecgca811 (22 + 1)a ecgca876 (22 + 1)a ecgca900 (22 + 1)b ecgca274 (23 + 6)a ecgca300 (23 + 6)a ecgca649 (23 + 6)a
ecgca323 (23 + 6)a ecgca902 (23 + 6)b ecgca986 (23 + 6)a ecgca997 (23 + 6)b ecgca848 (24 + 2)a ecgca368 (24 + 2)a ecgca410 (24 + 2)a ecgca826 (24 + 2)a ecgca571 (25 + 0)a ecgca880 (25 + 0)b ecgca115 (27 + 6)b
ecgca252 (29 + 2)b ecgca816 (29 + 2)b ecgca308 (30 + 5)b ecgca621 (30 + 5)b ecgca864 (30 + 5)b ecgca127 (31 + 4)b ecgca384 (31 + 4)a ecgca436 (31 + 4)b ecgca699 (32 + 3)b ecgca868 (32 + 3)b ecgca998 (32 + 3)b
ecgca392 (33 + 4)a ecgca416 (33 + 4)b ecgca776 (33 + 4)b ecgca968 (33 + 4)b ecgca896 (34 + 6)b ecgca595 (35 + 6)a ecgca629 (35 + 6)a ecgca659 (35 + 6)a ecgca515 (37 + 1)b ecgca711 (37 + 1)b ecgca244 (38 + 0)a
ecgca290 (38 + 0)a ecgca733 (38 + 0)a ecgca585 (38 + 2)a ecgca597 (38 + 2)a ecgca886 (38 + 2)a ecgca444 (39 + 0)a ecgca840 (39 + 0)a ecgca746 (39 + 6)a ecgca771 (39 + 6)b ecgca473 (40 + 2)a ecgca906 (40 + 2)a
a b
A reasonable estimation. A failing estimation.
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Fig. 8 – FECG estimation by ACF using Ch3–Ch5 abdominal signals in Fig. 5.
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Fig. 9 – FECG estimation by ACF step by step using “ecgca826” signal recording at 24 gestational weeks plus 2 day.
Fig. 10 – A failure example for a low SNR signal “ecgca115” due to the fetal R-peak detection errors.
errors has been shown in the Fig. 10. Multiple channels fusion could be considered as a good solution for improving the R peaks detection. The authors would plan to detect the R peaks using multiple abdominal ECG signals in next research stage.
5.
Conclusion
The difference between the FECG and normal noise in abdominal signal is that the FECG is quasi-periodic, and the fundamental frequency of MECG and FECG is different.
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Therefore, the adaptive comb filter is suited to estimate the FECG form abdominal signal. The described algorithm is simple and robust, without limitations of the any particular recording technique. The single-lead feature is desirable from the comfort point of view of the patient especially during longterm monitoring.
Conflict of interest We declare that we do not have conflicts of interest.
Appendix A. Pseudo-code of the proposed method 1. 2.
load the abdominal ECG signals a(n) preprocessing 0.05–100 Hz band-pass FIR filter;
3. 4.
removing 50 Hz/60 Hz power line interference; detect the maternal R peaks in a(n); determine the unit sample response hm (n) of ACF for maternal ECG estimation: hm (n) =
Nk =
L
ak ı(n − Nk )
⎧ k=−L −1 ⎪ ⎪ ⎪ − Tl , k < 0 ⎪ ⎪ ⎪ ⎨ l=k 0,
⎪ k−1 ⎪ ⎪ ⎪ ⎪ Tl , ⎪ ⎩
k=0 k>0
l=0
maternal ECG estimation from a(n): mecg(n) = convolution (a(n), hm (n)); 6. obtain the residual ECG signal by r(n) = a(n) − mecg(n); 7. detect the fetal R peaks in r(n); 8. determine the unit sample response hf (n) of ACF for fetal ECG estimation: 9. fetal ECG estimation from r(n): fecg(n) = convolution (r(n), hf (n)); 10. end
5.
references
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