FASSNet: fast apnea syndrome screening neural network based on single-lead electrocardiogram for wearable devices

Pre-processing steps are designed to facilitate learning process of FASSNet. In this study, the sampling frequency of raw ECG signal is set to 100 Hz. Interpolation methods can be used if ECG segments are of different sampling frequencies. The data pre-processing scheme is illustrated in figure 2. Signal smoothing is the first step. High-quality RR waves have proved useful in previous studies (Sannino et al 2014, Nakayama et al 2019). Hence, we adopt a Chebyshev type-II low-pass filter, which produces trimmed RR waves by smoothing raw ECG signal. Spectrograms of 60 s ECG segments are selected in view of their well-practised effectiveness (Jarvis and Mitra 2000, McNames and Fraser 2000). They are calculated on the basis of power spectrum density via STFT, and provide spectro-temporal patterns of SA syndromes. Baseline wander removal is performed during STFT. High-frequency components in a typical ECG epoch are negligible after signal smoothing (figure 2). Yu et al demonstrated that they are redundant in abnormal diagnosis (Yu et al 2019). Hence, we conclude that high frequencies in ECG signal are redundant for SA syndrome screening, and removing them has a limited adverse influence on accuracy. Removing high-frequency part of spectrogram reduces the size of model input, which contributes to reducing computation cost. A 'preserve-edge-information' design is realised to select the input size along frequency axis on the basis of the cut-off frequency (Fs) for signal smoothing. The upper bound frequency of model input is marginally higher than the Fs, which enables models to preserve-edge information with minimal input size. The mapping relation can be formulated as equation (1):

$$\begin{eqnarray}&&frequency\,input\,size=ceil\left(\displaystyle \frac{65\,{\rm{Fs}}}{100\,{\rm{Hz}}}\right)+1,\end{eqnarray} \tag{ 1 }$$

where 65 is the maximum position index of the frequency array in the spectrogram, and the $ceil(\cdot )$ operation returns the minimum integer which is larger than the input. There will be misleading spectrogram patterns when ECG signals are completely missing. To avoid wrong feedback in model training process, we eliminate epochs with signal absence if they are of low standard variation.

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The FASSNet architecture is shown in figure 3. The model comprises two stages, namely local spectrogram pattern and long-range information learning. Convolutional layers extract features automatically during the local spectrogram pattern learning stage. In the long-range information learning process, we prioritise position information along frequency bands for application of bidirectional long-short-term memory (Bi-LSTM) blocks to avoid redundant computation along time axis. Because there is no need to identify the onset of an SA event during minute-to-minute SA syndrome screening, whilst distinguishing high- and low-frequency bands contributes to providing effective features (Ravelo-Garcia et al 2015, Varon et al 2015, Song et al 2016). Layer normalisation is a key component of FASSNet that substantially improves classification performance with low computation cost. It gives us insight to design a robust model for SA syndrome detection.

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2.2.1. Local spectrogram pattern learning

2.2.2. Long-range information learning

Convolutional layers are insensitive to the location of its input (Liu et al 2018). It suggests that position information of spectrogram in our convolution outcomes is insufficient. Position information is unevenly distributed along time and frequency axis in the spectrogram (figure 2). High-frequency noise can have the same negative impact as low-frequency noise if no position information of frequencies is provided. Furthermore, confusing low and high-frequency components of a ECG segment may lead to a misleading diagnosis of FASSNet. In contrast, location information along the time axis in CNN output is less important, because a short ECG segment of Apnea-ECG recordings can be classified as an apnea epoch without providing information about the exact time of an SA syndrome event onset. Therefore, Bi-LSTM network and attention layer are implemented along frequency axis to bring long-range frequency correlations to model decision. The Bi-LSTM is a concatenation of forward and backward long-short-term memory (LSTM), as shown in equations (2)–(5), and the attention layer is expressed in equations (6)–(7):

$$\begin{eqnarray}&&{o}_{t}^{f},\,{h}_{t}^{f},\,{c}_{t}^{f}=LST{M}^{f}\left({h}_{t-1},\,{c}_{t-1},\,{x}_{t}\right),\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{o}_{t}^{b},\,{h}_{t}^{b},\,{c}_{t}^{b}=LST{M}^{b}\left({h}_{t+1},\,{c}_{t+1},\,{x}_{t}\right),\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{o}_{t}={o}_{t}^{f}| | {o}_{t}^{b},\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{h}_{t}={h}_{t}^{f}| | {h}_{t}^{b},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&attention\,weight=softmax\left({o}_{t}\times {h}_{t}\right),\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&attention\,outputs={o}_{t}^{T}\times attention\,weight,\end{eqnarray} \tag{ 7 }$$

where $LST{M}^{f}$ and $LST{M}^{b}$ denote forward and backward LSTMs, respectively. LSTM (Hochreiter and Schmidhuber 1997) takes an N-length data sequence $\left\{{x}_{t},\,t=0,\,1,\,2,\,3,\ldots ,\,N\right\}$ as input. Their outputs ${o}_{t}^{f}$ and ${o}_{t}^{b}$ contain the output features ${h}_{t}^{f}$ and ${h}_{t}^{b}$ from the last LSTM layer. The LSTM cell states are denoted as ${c}_{t}^{f}\,\,$and ${c}_{t}^{b},$ which control the information flow and preserve long-range information. $LST{M}^{f}$ leverages past information ${h}_{t-1}^{f}$ and ${c}_{t-1}^{f}$ to determine current feature, and $LST{M}^{b}\,\,$leverages future information ${h}_{t+1}^{b}$ and ${c}_{t+1}^{b}.$ Bi-LSTM is powerful in extracting both forward and backward contextual information (Graves et al 2005). In FASSNet, the input sequence of Bi-LSTM is along the frequency axis. The spatial relation of low- and high-frequency components of ECG spectrogram is learned. Soft attention block (Bahdanau et al 2014, Xu et al 2015) assigns weights ranging in [0, 1] according to the importance of the regions of input. It provides in-epoch information about the exact time interval at which an apnea event is likely to occur according to $LST{M}^{b}$ and $LST{M}^{f}.$

2.2.3. Layer normalization

The sensitivity of gradients with respect to weights in one hidden layer to outputs of the previous layer is an undesired property in training DNNs (Ba et al 2016). Mean value $\mu$ and standard variance ${\sigma }^{2}$ for normalising the output $X\in {R}^{C\times H\times W}$ of a layer are defined as equation (8)

$$\begin{eqnarray}&&\mu =\displaystyle \frac{\displaystyle {\sum }_{x\in X}x}{C\times H\times W},\,{\sigma }^{2}=\displaystyle \frac{\displaystyle {\sum }_{x\in X}{\left(x-\mu \right)}^{2}}{C\times H\times W},\end{eqnarray} \tag{ 8 }$$

where $C$ is the channel axis and both $H$ and $W$ are spatial axes. If a lengthy event activates additional apnea-sensitive neurons in hidden layers, then the layer-wise output will be accurately normalised by a larger mean value according to the layer normalisation. The proportion of apnea duration is a segment-wise property. Therefore, we abandon the commonly used batch normalisation (Ioffe and Szegedy 2015), where mean values typically come from multiple records in the same batch. Layer normalisation promotes the robustness of FASSNet. We discuss the effect of layer normalisation in section 2.4.2.

Two sets of criteria are included in evaluating model performance. We introduced accuracy (Acc), specificity (Spe), sensitivity (Sen), F1 score (F1) and area under receiver operating characteristics curve (AUC) to describe the classification performance. Meanwhile, value of model parameters (Params) and multiply accumulates (MACs) in an inference are used to measure real-time performance, because they indicate the algorithm applicability to hardware constraints. Classification performance measurements are expressed as equations (9)–(12):

$$\begin{eqnarray}&&Acc=\,\displaystyle \frac{TP+TN}{TP+TN+FP+FN},\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&Spe=\,\displaystyle \frac{TN}{TN+FP},\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&Sen=\,\displaystyle \frac{TP}{TP+FN},\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&F1=\,\displaystyle \frac{2TP}{2TP+FP+FN},\end{eqnarray} \tag{ 12 }$$

where TP, TN, FP and FN are quantities of true positives, true negatives, false positives and false negatives, respectively. SA syndrome epochs are positives in our systems.

AUC is used for determining the hyper-parameters of FASSNet. It is calculated by accumulating the area under a receiver operating characteristics (ROC) curve. An ROC curve takes false positive rate (100%-Spe) at different classification thresholds as horizontal axis and true positive rate (Sen) as vertical axis.

There are two real-time metrics to evaluate whether a model for wearable devices is light-weight or not. Params measures memory allocations. The MAC operation is defined in equation (13)

$$\begin{eqnarray}&&A\,MAC\,operation:a\leftarrow a+b\times c,\end{eqnarray} \tag{ 13 }$$

where $a,$ $b,$ and $c$ are floating numbers. MACs is one of the standard measures to evaluate computation cost in model inferences. The real-time performance of neural networks is calculated by summarising the Params/MACs of each block.

2.4.1. Dataset

The open-source Physionet Apnea-ECG database is used in this study. Table 1 provides the notations of 70 recordings from 32 subjects and their demographic information, and the recording-wise information is available in the appendix. Subjects were between the ages of 27 and 63 and between the BMI of 19.20 and 45.33 kg m⁻². Each recording contains a 100 Hz single-lead ECG signal digitised at 12 bit resolution, with a length of approximately 7–10 h. Each recording includes reference annotations for each minute of ECG segments (Goldberger et al 2000, Penzel et al 2000). Each 60 s ECG segment is labelled as a $Non \mbox{-} apnea\,minute$ or an $Apnea\,minute.$ In apnea-ECG, an $Apnea\,minute$ contains one or more apnea events or hypopnea events. However, the number of apnea and hypopnea events for each minute is not given. Hence, instead of using AHI defined in AASM standard (equation (14)), we adopted a common AHI computation approach as previous protocol (Penzel et al 2000), as shown in equation (15), to estimate SA syndrome severity. At present, all data and labels are publicly available.

$$\begin{eqnarray}&&AH{I}_{AASM}=\frac{60\times (Apnea\,Events+Hypopnea\,Events)}{Apnea\,minutes\,+\,Non \mbox{-} apnea\,minutes},\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&AH{I}_{Apnea \mbox{-} ECG}=\frac{60\times Apnea\,minutes}{Apnea\,minutes\,+\,Non \mbox{-} apnea\,minutes}.\end{eqnarray} \tag{ 15 }$$

Table 1. Apnea-ECG recordings and demographics ^a .

Subject ID	Recordings	Subject ID	Recordings	Subject ID	Recordings	Subject ID	Recordings
01	a01,	09	a09,	17	b05,	25	c10,
	a14		a18		x11		x18
02	a02,	10	a11	18	c01,	26	x02
	x14				x35
03	a03,	11	a15, x27,	19	c02,	27	x06,
	x19		x28		c09		x24
04	a04,	12	a17,	20	c03,	28	x09,
	a12		x12		x04		x23
05	a05, a10,	13	a19, x05,	21	c04,	29	x10,
	a20, x07		x08, x25		x29
06	a06,	14	b01,	22	c05,	30	x13,
	x15		x03		x33		x26
07	a07, a16,	15	b02, b03,	23	c06	31	x17,
	x01, x30		x16, x21				x22
08	a08, a13,	16	b04,	24	c07,	32	x31,
	x20		c08		x34		x32
Demographics of all 32 subjects
Length minutes: mean (std)	Non-apnea minutes: mean (std)	Apnea minutes: mean (std)	AHI $\geqslant \,\,\,$5 : %	Age, year: mean (std)	Female gender : %	BMI, kg m−2 : mean (std)
1075.9 (426.4)	670.7 (362.4)	405.2 (434.1)	50	43.88 (10.86)	21.9	28.24 (6.90)

^a During the Physionet challenge 2000, the labels of 35 recordings with a prefix 'x' was unreleased. Some previous studies also excluded these recordings, as shows in table 2. Currently, the labels of all 70 recordings is available.

2.4.2. Experiment protocols

2.4.3. Experiment setup

Table 2 shows the classification results of ten-fold validation. Hand-craft-features like Hassan and Haque (2017) and Zarei and Mohammadzadeh Asl (2020) are the most effective, the best method is from Zarei and Mohammadzadeh Asl (2020), whose per-segment accuracy is 93.90%. FASSNet (38 Hz, 64) achieves an accuracy, sensitivity, specificity, and F1 of 86.41%, 77.96%, 91.74%, and 81.61%, and the accuracy of the most light-weight version of FASSNet can reach 85.61%. It outperforms a series of commonly used SA syndrome detection approaches in classification performance and has the highest accuracy among DNNs. In comparison, the accuracy of the Deep ResNet is 83.03% (Wang et al 2019a), and DNN features proposed by Li et al (2018) is 84.7%. Notably, classification performance alone is insufficient to decide a feasible model for portable devices. For instance, Surrel et al (2018), reported an F1 score which is slightly lower than previous researches. However, the algorithm has been competitive for wearable devices since 2018, where trade-offs between classification and real-time performance are required.

FASSNet scores the best accuracies in each fold, as shows in table 3. The accuracy is 86.4% when test subject set is {10, 11, 12, 14, 24}. However, the accuracy drops to 70.8% when patient 10 is the only test subject. It can be seen that the accuracy FASSNet is over 15% higher than that of Wang et al (2019a) when no information of subject 15 is available, which is an evidence that features from FASSNet are robust. For some subjects, the accuracy can be extremely high (subject 14 and subject 24). The polarization of classification performance in different patients is also observed in table 4. The test results of some patients can have an over 95% per-segment accuracy (subject 22–25), and the overall diagnosis of AHI severity is almost perfect. However, FASSNet fails to classify ECG segments of some patients such as subject 09 and 30. A possible reason is the heterogeneity of ECG patterns. According to table 1, $AH{I}_{AASM}$ and $AH{I}_{Apnea \mbox{-} ECG}$ of these patients are considerably different, which may introduce errors. Through comparing the results with previous studies, we can tell that FASSNet is an excellent method in SA syndrome screening task from the perspective of classification performance. The polarization of test results demonstrates the importance of patient-agnostic validation in testing SA syndrome screening algorithms.

According to table 5, FASSNet (38 Hz, 64) using 0.2% of parameters of AlexNet, which is a small neural network in image classification tasks (Krizhevsky 2014). Moreover, it has 4.17% of MACs of the deep ResNet in FASSNet (Wang et al 2019a), which is a remarkable improvement in real-time performance. As to hyper-parameter selection, the complexity of FASSNet quadruples when its width doubles or its input size quadruples. This finding indicates that the width is a dominant factor for model complexity compared to the input size. Temporal-frequency components of 28–38 Hz contain most of useful information to diagnose SA syndrome, whilst providing elements of 38–48 Hz shows very limited improvement. This evidence is consistent with the phenomenon in figure 2 that few spectral-temporal patterns are visible in the 38–48 Hz frequency band.

We discussed the influence of Fs in low-pass filtering and width w in FASSNet convolutional layers using a grid search method. Fs candidates are 28, 38 and 48 Hz, and the width candidates are 32, 64 and 128 kernels. According to the 'preserve-edge-information' design in section 2.2, input sizes are $20\times 92,$ $26\times 92$ and $33\times 92.$ The optimal duration of a single pixel from the spectrogram pattern learning outputs is explored by removing a convolution layer in the pre-activation block or a convolution block. The duration edges down when there is only one convolution layer in the pre-activation block, and removing a convolution block results in a significant decline. Figure 4 shows the AUC scores on the test set in 10-fold validation. In this study, we select FASSNet (Fs = 38 Hz, width = 64) as an optimal model for wearable devices, because it has the highest AUC score with low MACs and Params (table 5). FASSNet (28 Hz, 32) is an extremely light-weight solution to wearable devices. A small decline in the duration of the pixel of spectrogram patterns results in slightly weaker model performance, whilst a significant decrease makes the performance degeneration evident.

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Layer normalisation prevents the model from overfitting. It uses sample-dependent mean and standard value to align features in different samples. In our view, the randomness of occurrence and the variable duration of an apnea event are partly responsible for the heterogeneity among samples. FASSNet uses layer normalisation to cope with the situation, thereby screening SA syndrome accurately. Layer normalization significantly improves the classification performance of FASSNet. FASSNet scored an accuracy of around 70% in the test set in the ten-fold validation process if it used batch normalization instead. The design of layer nomaliasation adapts to the randomness of SA syndrome, which makes FASSNet a reliable model.

In FASSNet, forward and backward LSTM use forward and backward information to detect SA syndrome events. The subsequent attention block assigns importance to the position information of LSTM outputs. For apnea epochs, LSTMs are expected to focus on the same period, which shows that both LSTMs can detect the onset of an apnea event. For epochs where all the in-epoch periods are normal, we expect to see the divergence to define a normal state from attention weights of the two LSTMs. Because it indicates the intrinsic heterogeneity of FASSNet, a good sign of robustness. The kernel density of attention weights of per-segment labels is visualized in figure 5. Attention weight distributions of apnea segments are concentrated in small areas and consistent with similar Gaussian distributions. It indicates that both forward and backward information are unanimous in the most likely period of an apnea event. In contrast, attention weights of normal segments distribute in a random way. They are dispersed at edge, where the position index is 0 or 5. It is likely because there is no 'abnormal event' in 'normal state' at any time point, and central pixels receive additional attention in convolution and max-pooling operations.

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Compared to light-weight algorithms on wearables (e.g. Sannino et al 2014, Surrel et al 2018), the chief advantage of FASSNet (Fs = 38 Hz, width = 64) is excellent classification performance (Acc = 86.41%, Sen = 77.96%, Spe = 91.74%, F1 score = 81.61%). And compared to current DNNs (e.g. Wang et al 2019a), diagnosis of apnea screening through FASSNet requires extremely low computation cost (MACs = 90.188 M, Params = 0.115 M). The accuracy of FASSNet shows an upper trend with an increasing volume of training set despite patient-agnostic validation is more difficult than ten-fold validation (tables 2 and 4). It indicates that FASSNet benefits from the expansion of database as typical deep networks. The architecture of FASSNet is a robust, since it takes the characteristics of SA syndrome into account. Theoretically, FASSNet possesses a strong rejection ability to high-frequency disturbance because only low-frequency components are considered as model input. Moreover, an empirical evidence is that changing hyper-parameters of FASSNet causes only slight classification performance degradation (figure 4). The light-weight design and reliability of FASSNet make it applicable to various scenarios for wearable devices.

However, there are some drawbacks in FASSNet compared to previous approaches if we assume that computation cost is not a gap. Some computer-aided neural network (Li et al 2018) and feature-based method (Zarei and Mohammadzadeh Asl 2020) show higher accuracies (table 2). Patient-agnostic validation shows that the diagnosis of some patients can be unsatisfactory even models possess high accuracies in cross validation. For instance, the accuracy of subject 10 is 70.8% (see table 3), and the diagnosis of apnea severity of subject 09 is wrong (see table 4). Surrel et al (2018) also reported the same performance deterioration in certain patients. They suggested capturing subject-specific information since subjects vary demographically in ways that induce different ECG morphological patterns. For example, Laureanti et al (2020) documented that ECG parameters show statistical differences in gender. These findings demonstrate the necessity of patient-agnostic validation. Thereby, evaluation on more large-scale databases is important before implementing FASSNet on wearable devices. Furthermore, Apnea-ECG is a database released in the year 2000, and we need to update FASSNet according to recent AASM standard.

Large-scale modern datasets contribute to obtaining reliable models. Feeding more data to FASSNet can improve model performance without introducing additional computation loads. Considered that the architecture of FASSNet is robust, it is promising to apply it to other physiological signals. For instance, a dataset of 86 recordings from a hospital was used to evaluate a CNN model (Urtnasan et al 2018). Airflow signal recordings from clinical and MIT-BIH PSG database (Ichimaru and Moody 1999) are sufficient to train LSTM (Yang et al 2019). The optimal hyper-parameters of FASSNet need to be fine-tuned when input signal is different.