4.3 Time-varying AR spectrum computation
4.3.2 Time-varying AR modeling
As explained above, the FHR signal dynamics of interest involve highly complex character-istics mainly associated with nonlinearities as a result of the physiological regulation mech-anisms modulated by the ANS, which is highly variant in time. As explained in the example presented in Section 4.1.2, in the presence of such signal dynamics, the classical stationary version of AR modeling is no longer suited for their analysis. Therefore, in our proposed approach, we use the time-varying version of AR modeling, which can be appropriate for the FHR signal analysis since its parameters are now time-dependent. The TV-AR paramet-ric model can be represented by Eq. (4.5), where the AR parametersai,k(n){k=1, 2, ...,p}
are now the time-dependent coefficients, which correspond to a set of valuesai,k that is updated sample-by-samplen.
IMFi[n]= −
p
X
k=1
ai,k(n)IMFi[n−k]+e[n] (4.5) From Eq. (4.5), analogously to Eq. (4.3), the TV-AR model transfer function represented by:
44 CHAPTER 4. SIGNAL PROCESSING TECHNIQUES: THEORETICAL BACKGROUND
Hi[z,n]=I M Fi[z,n]
E[z,n] = 1
1+Pp
k=1ai,k(n)z−k (4.6) Then, the TV-AR spectrum can be expressed as:
S ARi(f,n)= σ2
¯
¯1+Pp
k=1ai,k(n)e−j2πf k¯
¯
2 (4.7)
This last equation (Eq. (4.7)) allows performing a spectral time-variant analysis since the computed spectrum not only depends on the frequency-domain but also on the time-domain.
For a more in-depth explanation of the AR modeling method, please refer to Abramovich et al. (2007), Kay and Marple (1981) and Pardey et al. (1996).
All the signal processing techniques presented above will be employed for the analysis of the modulated dynamics involved in the FHR signal, as explained in the next chapters.
Studying the FHR dynamics by ICEEMDAN and 5
TV-AR: Concepts
In order to answer the proposed research questions and reach the objectives of this thesis work (see Section 1.2), we propose to investigate the FHR signal dynamics resulting from the ANS modulation (signal dynamics of interest) and analyze their connection with the fetal health condition. The main idea is to track these dynamics of interest as observation of the process involved in the activity of the physiological behavior of the fetal compen-satory mechanisms (physiological phenomenon explained in detail in Section 2.1). For this purpose, we propose the signal feature extraction strategy presented in Fig. 5.1. As can be observed in this diagram, firstly, a preprocessing step is applied to the FHR and UC signals. This step involves both signal outliers removal and signal interpolation in order to deal with artifacts and sensor contact interruption involved in the CTG signal acquisition.
Secondly, we identify the FHR deceleration episodes based on aprogressive baselineand UC events. As explained in Section 1.1, the FHR decelerations are considered as one of the main patterns that can involve significant information about fetal distress. However, at the same time, they are the most difficult patterns to interpret by the clinical staff (Hruban et al., 2015; Spilka et al., 2014b). Therefore, we propose to identify and study the decelera-tion episodes together as well as independent from the complete FHR signal to investigate their contribution to CTG assessment. Thirdly, the FHR signal is detrended and decom-posed by ICEEMDAN, whose extracted IMFs are the input of the last signal processing step corresponding to the TV-AR spectral estimation. Finally, as shown in Fig. 5.1, the feature extraction operation is performed based on information in the time-domain as well as in the frequency-domain. All of these steps are described in this chapter, which explains the foundations behind the proposed strategy and its significance for our proposed approach.
For a better explanation of the concepts involved in the proposed strategy, we explain it step-by-step making use of the CTG recording shown in in Fig. 5.2, which corresponds to the recording no. 1179 extracted from the CTU-UHB database (Chudáˇcek et al., 2014).
5.1 CTG signal preprocessing
In signal processing, mainly in the area of biomedical signal processing, a preprocessing step is essential because an appropriate signal analysis depends significantly on the quality
45
46 CHAPTER 5. STUDYING THE FHR DYNAMICS BY ICEEMDAN AND TV-AR: CONCEPTS
Signal processing
Signal detrending Deceleration
detection ICEEMDAN TV-AR
spectrum
Feature extraction FHR
Progressive Baseline UC
CTG database
Signal preprocessing
Figure 5.1: Block diagram of the strategy proposed for the CTG signal feature extraction.
1000 1500 2000 2500 3000 3500 4000 4500
50 100 150
FHR [bpm]
time [s]
(a)
1000 1500 2000 2500 3000 3500 4000 4500
0 20 40 60 80 100
UC [mmHg]
time [s]
(b)
Figure 5.2: CTG recording no. 1179 extracted from the CTU-UHB database. (a) Raw FHR signal; (b) Raw UC signal.
5.1. CTG SIGNAL PREPROCESSING 47 of the input data. Particularly, the CTG signal acquisition usually involves different types of artifacts such as loss of data and signal outliers, mainly produced by the mother’s move-ments and loss of sensor’s contact that can temporarily interrupt the signal acquisition. In order to deal with these acquisition problems, we apply a preprocessing step for both the FHR and UC signals to prepare them for the subsequent analysis.
On the one hand, for the FHR signal, the artifact rejection method proposed by Spilka et al.
(2013) is applied, which consists of two main steps: outliers removal and signal interpola-tion. In the outliers removal step, FHR signal values considered physiologically inconsis-tent in amplitude, i.e., values outside the range between 50 bpm and 210 bpm, are removed from the signal. Then, in the FHR signal interpolation step, loss of signal data correspond-ing to segments of length equal or less than 75 s are interpolated by uscorrespond-ing a Hermite spline method.
On the other hand, for the UC signal, loss of data less than 25 s are interpolated, and then the UC signal is filtered by a moving average filter of 15 s windows length. Note that this filtered UC signal is used for the decelerations characterization, as explained in Section 5.2.
Fig. 5.3 shows an example of the resulting preprocessed FHR and UC signals computed from the CTG signals presented in Fig. 5.2.
1000 1500 2000 2500 3000 3500 4000 4500
50 100 150
FHR [bpm]
time [s]
(a)
1000 1500 2000 2500 3000 3500 4000 4500
0 20 40 60 80 100
UC [mmHg]
time [s]
(b)
Figure 5.3: Preprocessed FHR and UC signals computed from the CTG recording no. 1179 presented in Fig. 5.2(a) and (b), respectively.
It is important to note that the obtained preprocessed FHR signal is used only for the FHR baseline estimation and identification of FHR deceleration episodes (explained be-low). The signal detrending and subsequent signal processing operations are performed by using the raw FHR signal only after the outliers removal step.
48 CHAPTER 5. STUDYING THE FHR DYNAMICS BY ICEEMDAN AND TV-AR: CONCEPTS