A deep learning approach for fetal QRS complex detection

Data used in this experiment are collected from set-a of PhysioNet/computing in the cardiology challenge database (PCDB) (Silva et al 2013). PCDB is the largest publicly available NI-FECG dataset to date. Set-a includes seventy-five abdominal ECG (AECG) recordings (a01–a75). Each recording includes four channels. Each channel is sampled at 1000 Hz. Data and reference annotations (fetal QRS complexes) for set-a are available. As suggested in Behar et al (2013), seven AECG recordings (a33, a38, a47, a52, a54, a71 and a74) are discarded because of inaccurate reference annotations.

The remaining 68 AECG recordings without a signal quality assessment implementation described below are divided into three categories: training, validation, and testing sets. Seven recordings (a01, a02, a03, a04, a05, a06 and a07) constitute the testing set, which includes a total of 3924 fetal QRS complexes. Six recordings (a08, a09, a10, a11, a12 and a13) constitute the validation set, which includes a total of 3348 fetal QRS complexes. The remaining 55 recordings constitute the training set, which includes a total of 31 056 fetal QRS complexes. Notably, the data for the training, validation, and testing sets are mutually exclusive.

Automatic high-accuracy methods for adult QRS detection (thus maternal QRS) have been published since the mid-1980s (Pan and Tompkins 1985). However, methods for fetal QRS detection are still in their infancy. In the context of NI-FECG extraction, a detected fetal QRS is classically considered a true positive if it is within 50 ms of the reference annotation. So the frame size is set to 100 ms. An example of an input in this study is shown in figure 1.

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To form a relatively balanced dataset, a stride of 35 ms is implemented for data without fetal QRS and a stride of 10 ms is implemented for data with fetal QRS. In this study, fetal QRS detection is a task of binary classifcation. Each NI-FECG signal in the training, validation, and testing set is 100 ms long and can contain only one type. Each NI-FECG signal is annotated into one of the two classes according to the reference annotation provided by the PCDB. For each 100 ms long NI-FECG signal, if the reference location of the fetal QRS complex is within the frame, then the NI-FECG signal is considered a fetal QRS complex. In contrast, if the reference location of the fetal QRS complex provided by the PCDB is not within the frame, then we considered the 100 ms long NI-FECG signal not a fetal QRS complex.

We investigate the task of fetal QRS complex detection from the raw NI-FECG signals. This is known to be a challenging task and it is very common for the NI-FECG to be contaminated by a variety of other physiological signals and noise. To automatically detect fetal QRS complexes in NI-FECG signals, an algorithm must possess the ability to recognize the distinct wave types and discern the complex relationships between them over time. This is difficult due to the variability in wave morphology in the NI-FECG signals as well as the presence of noise from all kinds of interference sources. Thus, there is a need for effective techniques that can assess the signal quality of NI-FECG. The sample entropy (SampEn) method mentioned in Liu et al (2014) is used in this study for noise identification. The SampEn is defined as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm SampEn}(m, r, N) = -{\rm ln}(\sum_{i=1}^{N-m}A_i^m(r)/ \sum_{i=1}^{N-m}B_i^m(r)) \label{SampEn} \nonumber \end{align} \tag{ 1 }$$

where m corresponds to the embedded dimension, r to the threshold and N to the data length. To get more details about the SampEn, the article from Liu et al (2014) is recommended. In this study, the threshold is set at 1.5. The embedded dimension is set at 2 and the data length is set at 500. By comparing the mean SampEn value from each channel with the threshold value, SampEn values less than 1.5 are regarded as good quality and are used in the study. However, if the number of good quality signals is less than two in a recording, the two channels with the smallest and penultimate SampEn values are obtained to form the dataset. An example of signal quality assessment on a 10 s signal episode from record 42 of set-a is shown in figure 2.

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After signal quality assessment, the number of fetal QRS complexes in training, validation, and testing sets change to 26 639, 3082 and 3538, respectively. A three-layer convolutional neural network is trained on this training set. The network maps a sequence of NI-FECG samples to a sequence of sample classes.

With large annotated datasets, deep neural network based machine learning models have consistently been able to approach and often exceed human performance (He et al 2015, Amodei et al 2016). The CNN is a trainable and non-linear system that is made up of a very large number of connections and layers. It has already proven to be effective in many fields such as handwriting character recognition and healthcare applications, particularly in arrhythmia detection and medical imaging (Rajpurkar et al 2017, Esteva et al 2017).

The fetal QRS complex detection task is a sequence-to-sequence task. A CNN model is employed for this sequence-to-sequence learning task. An NI-FECG signal $X= [x_1, x_2, ..., x_s]$ is the input to the model. A sequence of labels $P=[\,p_1, p_2, ..., p_n]$ are the output of the model. Each segment of the input corresponds to an output label.

The convolutional layers calculate L 1D convolutional computations between filter vectors w^l, of size 2k  +  1, and input map x:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle y^l(i) = \sum_{j=-k}^{k }w^l(\,j)x(i - j) ~~l=1, 2, ..., L \nonumber \end{align} \tag{ 2 }$$

where y^l(i) is the unit i of the l-th output feature map and w^l(j) is the weight j of the l-th filter vector. The dimension (dim) of the output feature map (y) is defined as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm dim}(y) = \frac {{\rm dim}(x) - {\rm dim}(w) + 1}{{\rm size~ of~`max~pooling'}}. \nonumber \end{align} \tag{ 3 }$$

Then the output units of the convolutional layer are given by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle z^l(i) = {\rm ReLU}(y^l(i) + b^l)~~l=1, 2, ..., L \nonumber \end{align} \tag{ 4 }$$

where z^l(i) is the unit i of the l-th output units of the convolutional layer and where b^l is the bias term.

The ReLU activation function is represented by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle f_{r}(v) = {\rm max}(0, v). \nonumber \end{align} \tag{ 5 }$$

We use a cross-entropy objective function as the loss function in this study. The cross-entropy objective function is given by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \mathcal{L}(Q, P) = - \sum_{i=1}^{n }Q(i) \log P(i) \nonumber \end{align} \tag{ 6 }$$

where Q is the ideal output and where P is the actual output.

Figure 3 shows the high-level architecture of the proposed deep learning network. Overall, the architecture of the network contains three convolutional blocks and a dense block. The first convolutional block contains a convolutional layer (Conv1), a batch normalization (Ioffe and Szegedy 2015) layer (BN1) and an activation function layer (ReLU1). In the first convolutional block, we apply the BN1 between the Conv1 and ReLU1 to make the optimization of such a deep CNN model more tractable.

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The second convolutional block contains a convolutional layer (Conv2), a dropout layer (Dropout2), a max-pooling layer (Maxpool2) and an activation function layer (ReLU2). In the second convolutional block, we apply the Dropout2 and Maxpool2 between the Conv2 and ReLU2 to prevent neural networks from overfitting.

The third convolutional block contains a convolutional layer (Conv3), a dropout layer (Dropout3), a max-pooling layer (Maxpool3) and an activation function layer (ReLU3). The convolutional layers are considered as a feature extractor, which capture the abstraction of NI-FECG signals.

The dense block contains dense layers (Dense) and a softmax layer (Softmax). The Dense contains three fully connected layers. A distribution over the two output classes (number of classes n  =  2 in this study) is produced by final fully connected layers and softmax.

The proposed deep learning network, which contains three convolutional layers (L  =  3), takes as input a time-series of 100 ms long NI-FECG signals (input length s  =  100 in this study). The first, second, and third convolutional layers contain 64, 128, and 256 filters, respectively. Each filter generates one feature map. Inspired by some convolutional neural network models (Simonyan and Zisserman 2014), the filter length used in this study is set at 3. Using the filter with length of 3 achieves satisfactory results in this study, and we have not found significant performance improvement when using a larger filter. The size of all the max-poolings is set at 2. We use the stochastic gradient descend optimizer with learning rate 10⁻² to train the model in this study. Overall, the CNN network maps a sequence of NI-FECG samples to two sample classes (fetal QRS or not fetal QRS). In addition, the data is normalized before the raw NI-FECG signal is fed into the CNN network. The min-max normalization is used to transform the data into a common range $[0, 1].$ We use the validation set to evaluate the model and the best model is saved during the optimization process.

In the proposed method, the features of single-channel NI-FECG signals are used for fetal QRS complex detection. In the case of multi-channel signals, the channel with the best quality is recommended for the detection task. In addition, in order to learn more possible patterns present in the data, the channels with relatively good quality (SampEn values less than 1.5) are used to train the CNN network in this study.

Precision, recall, and F-measure are typically used as the evaluation metrics in pattern recognition and information retrieval. We use these evaluation metrics to assess the performances of fetal QRS complex detection. Precision, recall, and F-measure are defined as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Precision = \frac {TP}{TP+FP}} \nonumber \end{align} \tag{ 7 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Recall = \frac {TP}{TP+FN} }\nonumber \end{align} \tag{ 8 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle F_{1}~{\rm measure= 2\times \frac {Precision \times Recall}{Precision + Recall}} \nonumber \end{align} \tag{ 9 }$$

where TP, FP, and FN are the number of true positive (correctly detected fetal QRS complexes), the number of false positive (wrongly detected fetal QRS complexes) and the number of false negative (missed detected fetal QRS complexes) detections, respectively. Precision represents how good the algorithm is at detecting true fetal QRS complexes out of all the detections it makes. Recall represents how good an algorithm is at finding the true fetal QRS complexes. F-measure is also called F₁ measure and it is an harmonic mean that represents the equal weights of precision and recall. The performance of the classification processes is computed in terms of accuracy:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm Accuracy = \frac {TP +TN}{TP + TN + FP +FN}}. \nonumber \end{align} \tag{ 10 }$$

To confirm the effectiveness of CNN on fetal QRS complex detections based only on NI-FECG fingerprinting without canceling MECG signals, we compare our approach with three other state-of-the-art classifiers, namely KNN, NB and SVM on testing set.

In our study, experiments with KNN, NB and SVM classifiers are performed on the MATLAB platform. NB is used with default parameters. A Euclidean metric is used for distance calculation in the KNN classifier. For the SVM classifier, we adopt a Gaussian radial basis function as the kernel function. The parameters used in KNN, NB and SVM classifiers are all optimized on the validation set.

Figure 4 and table 1 demonstrate the experiment results for the fetal QRS complex detections of CNN versus the KNN, NB and SVM classifiers.

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We develop an algorithm that exceeds the classification performance of three other state-of-the-art classifiers in detecting fetal QRS complexes from raw data of NI-FECG signals. Considering precision, recall, F₁ measure and accuracy, CNN outperforms KNN, NB and SVM classifiers, demonstrating that the CNN network has better classification capability to effectively detect the fetal QRS complexes when compared with the three other classifiers.

In this study, the correlation between classification performance and signal quality assessment step is investigated. We use SampEn to assess the signal quality of the NI-FECG. So some channels with bad quality are excluded in the experiment. To test the effectiveness of signal quality assessment, experiments with/without signal quality assessment are employed in this study, and the results of with/without signal quality assessment are demonstrated in table 2.

Table 2 gives a comparison of the performance of two processes (with/without signal quality assessment) in accuracy. It is noted that better classification performance of the CNN classifier is obtained by implementing the SampEn based signal quality assessment procedure for the real AECG signals. In addition, it should be also noted in the equation (1) that the SampEn values mainly rely on the parameter setting of threshold r. In this study, only a small part of the channels with poor signal quality is excluded by setting the threshold to 1.5. In addition, some improved entropy methods are proposed with better algorithm stability and consistency (Liu et al 2013). With a combination of fuzzy theory and entropy, these new methods provide a new insight into assessing the signal quality of the NI-FECG and it is worth evaluating their effectiveness for fetal QRS complex detections in the future.

The NI-FECG is inevitably contaminated by baseline and power-line interference. In this fetal QRS complex detection task, we further test the effectiveness of removing baseline and power line interference. Firstly, a notch filter is used to remove power-line interference. Secondly, we implement a band-pass Butterworth filter between 0.5 Hz and 100 Hz to remove baseline wander interference. The band-pass Butterworth filter is cascaded by a second-order low-pass and a second-order high-pass filter, and we also implement zero-phase digital filtering to minimize start-up and ending transients in the NI-FECG signals.

The classification performance of classifiers with or without removing baseline and power line interference are tested in this study, and the results are demonstrated in figure 5

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Figure 5 gives a comparison of the two processes (with/without removing baseline and power line interference) in accuracy. Here, we can note that removing the baseline and power line interference slightly improves the performance of recognition in the CNN classifier, and very similar results are obtained in KNN and SVM classifiers. The fetal QRS complex detection task in this study can be considered as a kind of morphological analysis. The morphology of fetal ECG is enhanced by removing baseline and power line interference. In addition, we should perform the morphological analysis of abdominal signals in a different way, which depends on the established goal. For example, to detect the fetal QRS, filters should be projected to enhance this complex and to reduce other waves such as T.

The features of morphology in NI-FECG signals are captured step by step in the CNN, and the performance of the CNN network is affected by activation functions.

In this study, we further test the effectiveness of activation functions on the fetal QRS complex detection task. Three kinds of activation functions including sigmoid, hyperbolic tangent (Tanh), and rectified linear unit (Relu) are tested in this study. The sigmoid activation function is defined as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle f_s(v) = \frac{1}{1 + \exp(-v)} \nonumber \end{align} \tag{ 11 }$$

and the Tanh activation function is represented by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle f_t(v) = \frac{{\rm exp}(v) - {\rm exp}(-v)}{{\rm exp}(v) + {\rm exp}(-v)}. \nonumber \end{align} \tag{ 12 }$$

The results of different activation functions are demonstrated in table 3. Here, we can note that ReLu outperforms the other two activation functions in this study. So the ReLu is highly recommended on this particular task.