Permutation entropy of fetal heart rate with extraction of maternal heartbeats

Development and application of maternal and fetal physiological states identification techniques based on the noninvasive electrical heart activity monitoring is of great clinical importance during pregnancy. In this paper, new possibilities of applying one of nonlinear measures of time series behavior analysis to the fetal heart rates are explored, and permutation entropy (PE) characteristics of fetal rhythmograms are used to get new insight on the fetal heart rhythm parameters. The new technique of fetal electrocardiogram (fECG) extraction is used, based on filtration in wavelet domain and reconstruction of fECG using detalization coefficients. Permutation entropy analysis is applied to obtain PE values and trends for the case of raw fetal rhythmograms and those obtained with excluded maternal heart beats. The assumption about the need to extract maternal heartbeats from initial rhythmogram is proven by the difference in PE values for two cases. Ref. 11, figs. 11.


Introduction
Development and application of maternal and fetal physiological states identification techniques based on the noninvasive electrical heart activity is directed to prediction and control of heart diseases on the early stage of pregnancy [1] and favored mainly from the high resolution recording and signal analysis technologies. Of main interest are the possibilities to detect fetal distress, hypoxia, breathing movements, fetal heart functioning and other, to identify possible deviations and/or diseases in fetus development. Many researchers have been developing new techniques for fetus and mother state evaluation using various noninvasive modalities such as electrocardiography, Doppler ultrasound, MRI etc. The main focus is on the fetal heart rate analysis [4][5][6] for assessment of fetal development, prenatal diagnosis, and autonomic nervous system functioning during pregnancy.
The goal of this paper is to study the permutation entropy (PE) characteristics of rhythmograms to get new insight on the fetal heart rhythm parameters. We have applied PE to the fetal heart rhythm calculated for two cases, dealing with the problem of potential presence of maternal R-peaks in the processed fetal electrocardiogram (fECG) and shown that there is significant difference for these cases.

Fetal heart beats detection
Despite of high level of medicine nowadays, estimation of prenatal normal and pathological states is far from its final solution because of the lack of our knowledge about fetal physiology and pathophysiology. Automated analysis of measured data can provide researchers and clinicians with objective information about fetus state and functioning. The most beneficial approach is the analysis of fetus heart beats, registered and detected by cardiotocography or fetal electrocardiography [9]. There are several characteristics of fetal heart beats [9] based on the interbeat intervals: − arrhythmicity levels of different types (oscillatory, linear, arrythmic); − basal frequency; − variability magnitude; − variability frequency; − accelerations and decelerations of different types (early, late, variable, prolonged). Estimation of electrical activity of fetus heart is an inherent diagnostic procedure during pregnancy. The most informative is the fetal ECG (fECG) signal which should be registered with high signal-to noise ratio. After registration of ECG signal containing mother and fetus activity (Fig.1), separation of fECG from maternal ECG should be done, based on the differences in their magnitude spectral, shape and other characteristics. Among the existing techniques to solve this task those based on wavelet transform and blind sourceseparation are the most effective [2,7,10].  In this paper the new technique of fECG extraction from the mixture of maternal and fetal ECGs is used. This approach is based on discrete wavelet analysis (DWT). First, appropriate mother wavelet function should be selected, which resembles the shape of fetal QRS complexes and thus allows its detection in abdomen ECG with higher accuracy.
After that abdomen ECG ( ) Approximation coefficients contain low-varying signal components, while detalization coefficient resemble high-frequency fluctuations. Noise components are concentrated in the detalization coefficients thus they should be processed in orderto remove high-frequency noise. To do this, the threshold should be chosen first, and then hard thresholding procedure is applied. After thresholding ECG is reconstructed using only detalization part of the appropriate decomposition level. This level is empirically optimized to obtain only fECG part in reconstructed signal.
Then simple geometric approach can be employed to get precise positions of fetal R-peaks: one needs to find starting and ending point of fetal QRS complex and then the time position of R-peak occurrence is assigned to time instant in the middle point. This approach can be used to extract fECG only owing to the fact that the reconstruction and filtration introduces the same delay into the processed ECG, thus the RR-peaks intervals will remain the same.
Another possibility to obtain rhythmogram is to process the recovered ECG signal after filtration.
Having the presumably only-fetal QRS-complexes singled-out, the next task is to choose and elaborate the R-peaks detection algorithm. One of the most robust and widely used algorithms is the Pan-Tompkins algorithm [8]. It starts from bandpass filtering. After applying the filter the signal is differentiated to provide the QRS-complex slope information. Then to obtain waveform feature information in addition to the slope of the R-wave the moving-window integration is used. And finally in order to get the R-peaks thresholding is applied. In the present paper the algorithm is implemented as is up to the thresholding part which should be remodeled for the case of amplitude-varied Rpeaks.

Permutation entropy of rhythmogram
The PE is a measure of disorder of information contained in comparing the consecutive values of the signal [3]. The PE shows the extent to which analyzed signal is random (chaotic). It is based on approaches of symbolic dynamics and uses the relative frequencies of various patterns encountered in signal samples. Such approach benefits from the fact that PE does not depend on signal values and uses only symbol sequence.
Permutation entropy of integer order m ( where ( ) q j is the number of occurrence of permutation j π .

Fig. 2. Patterns in signal for different time lags [11]
A more detailed mathematical foundations of the method`s calculation are given in the papers [1,3].
Embedded pattern thus consists of m different numbers (Fig. 3), which represent one of ! m possible permutations. Therefore each pattern can be considered as one of ! m permutation (Fig. 4), and is denoted , 1... ! j j m π =

Experimental results and discussion
In the Fig. 5 the results of fetal R-peaks detection procedure are presented. Obtaining a rhythmogram having the ECG with fetal constituents may be a challenging task due to the overlapping of fetal QRS complexes over the maternal ones. Since the maternal ECG signal is 3-15 times larger than fetal ECG special effort of distinguishing the QRS complexes should be made. To show this, we detected only maternal Rpeaks by standard technique (Fig. 6), and then removed them from the presumably fetal-only Rpeaks signal. After obtaining the signal with significantly less peaks, which are believed to belong to the fetal heart beats only (Fig. 7). Despite the fact that there is the possibility of maternal and fetal heart beats overlapping, the study if this is common satiation should be done. In the following, the two peaks sequences are analyzed: raw one (Set 1) and another with maternal peaks subtracted (Set 2). After that two rhythmograms were obtained using data from Set 1 and 2 (Figs. 8-10 respectively). Then PE for the rhythmograms of Set 1 and Set 2 as explained above for orders from 3 to 5 was calculated. Two approaches were used to PE calculation: first, we calculated one PE value for whole rhythmogram, obtaining one value for each order. PE trend for each rhythmogram with different time windows (TW=50 and TW=200 heartbeats) and then averaged PE values for all time windows were also calculated, resulting in one averaged PE value for each rhythmogram for each window duration. Typical PE trends for the case of order m=4 are given in Fig. 11

Fig. 11. PE trends for rhythmograms of Set 1 (top) and Set 2 (bottom), order m=4, time window is 50 heartbeats
It can be seen from Table 1 that fetal PE which is calculated for the whole signal is very close for the data from Set 1 and Set 2. The largest difference equal to 0.02 for 5th order, which is about 2 %. Thus it's hard to distinguish between the two sets using PE value for whole signal. In the case when PE trend was analyzed, there are different average values for two sets for various PE orders: PE for Set 2, where maternal heartbeats were removed, is less in general than for Set 1 where maternal heartbeats are presumably present. The largest difference is for order 5 for both of time windows durations. The most prominent difference in for the large time window TW=200 heartbeats and for order m=5: mean value for the Set 1 is 0.7, and for Set 2 is 0.88. Thus the assumption about the need to extract maternal heartbeats from initial R-peaks sequence can be proven by the difference in PE values for Sets 1 and 2.  Thus it might be feasible to subtract maternal heartbeats from the R peaks sequence when it is possible to detect peak from maternal ECG instead of fetal R peak. The study of entropy characteristics of fetal heart activity obtained by unmixing of fECG from composite abdominal ECG can be useful for diagnostics.

Conclusion
Combining the fetal and maternal ECG separation techniques with entropy analysis, one can acquire new insights on fetus heart activity. The new technique of fECG extraction is used in this paper, based on filtration in wavelet domain and reconstruction of fECG using detalization coefficients. Permutation entropy analysis is applied to obtain PE values and trends for different time windows and steps. The assumption about the need to extract maternal heartbeats from initial rhythmogram is proven by the difference in PE values for the fetal rhythmogram and fetal rhythmogram obtained after extraction of maternal R-peaks.