The analysis of electrocardiogram signal morphology based on convolutional neural network is considered. Input data is obtained by splitting the signal into cardiac cycles. The calculation the average cycle is performed to exclude the artefacts. The Haar wavelet transform of the average cycle is performed. The images of size 200x6 are input data for the recognition system: 200 - number of counts constituting the cycle; 6 - number of Haar transform time scales. This work is a reconsideration of the previous work of the authors. The training samples base of marked cardiac cycle segments is the same (1500 cycles): the average cycle and the segment's start and end indexes. In the previous work, the original composite system consisting of several modules was used as a recognition system. In current work it is proposed to use the convolutional neural network with the special structure: 4 convolutional layers, 2 dense layers, and 200 outputs for every of 3 segment. The recognition system based on neural network showed results slightly superior to the previous system. The percent of acceptable localization of the segments is the following: P - 82.2%, QRS - 88.7%, and T - 85.4%. The proposed system effectively solves the problem using the standard modules of modern artificial neural networks.
Among the many methods of research, observation and monitoring of human condition, the leading place belongs to electrocardiography (ECG). The need to monitor the ECG during anesthesia, resuscitation, intensive care and diagnosis is beyond all doubt. The ECG signal carries a large amount of information, and a detailed automatic analysis of the patient's ECG signal allows to timely generate alarms that prevent death, as well as to make prognostic conclusions.
When processing the ECG signal, taking the advantages of modern computing resources, it is
required to automatically analyze the shape of the ECG signal cycle (cardiocycle), i.e. automatically
recognize the characteristic segments and determine their time and amplitude parameters. [
An example of the ECG signal cardiac cycle shape and it’s characteristic points is shown in Fig. 1.
It is common in cardiology to analyze the segments, i.e. the regions between the characteristic points:
the segment of P (points P0… P1), QRS segment of a point (Q...S), and the segment T (point T0… T1).
The morphology analysis input receives information obtained at the stage of splitting the ECG signal
into cycles: an array of cardiocycle signals accumulated over a some period of time. [
MHAT wavelet tranform
Results of MHAT wavelet tranform Training Application
Manual markup
segments of cardiocycles Segments points of manual localization Calculation of statistical parameters
Statistical parameters of
segments Clustering of cardiocycle
segments Array of segments
classes Calculation of fuzzy
characteristics parameters of classes
Array of fuzzy characteristics parameters of classes
Calculation of statistical parameters of all samples
Statistical parameters of all
samples Calculating of fuzzy variables of classes The values of fuzzy variable of classes
and samples
Calculation of the conformity degree of classes and samples
The conformity degree of classes
and samples Determination of the maximum conformity
degree Time and amplitude parameters
Calculation of time and amplitude parameters
Class number
and segments
points localization
2. The previous version of the cardiac cycle morphology analysis
Based on the fact that the normal cardiocycle shape changes slowly over time and each current
cardiocycle can be distorted by artifacts and noises, it makes sense to recognize the characteristic
segments of average cardiocycle shape. The average cardiocycle of several (5-20) cardiocycles having
a high correlation coefficient with each other is calculated. Then the selected cardiocycles are
averaged pointwise. An example of the obtained signal is shown in Fig. 1 [
The training of the recognition system is performed on the basis of the information provided after
the manual cardiocycle marking, i.e. the localization of the start and end indexes of the segments P,
QRS, and T is known. Such information can be formed using specially developed software. Marking
of cardiocycles segments should be made by a medical specialist in this area. The screenshot example
of the software developed by LLC Izhtelemed for performing of such marking is presented on Fig. 2.
[
In [
Sample base of cardiocycles Training
Time and amplitude parameters
Manual markup
segments of cardiocycles Segments points of manual localization
Training of neural network Values of weight coefficients
Neural network Calculation of time and amplitude parameters
Haar wavelet tranform
Results of Haar wavelet tranform
Application of neural network
Application Segments points localization 3. The cardiac cycle morphology analysis based on neural network In this paper, a reconsideration of the approach based on the pattern recognition of the cardiocycle morphology is carried out, and it is proposed to use an artificial neural network (ANN) as a recognition system of cardiocycle segments. Fig. 4 presents the stages of morphology analysis based on convolutional ANN.
Currently, most studies on ECG analysis algorithms use wavelet transform [
2 +1 2 where x is the signal for which the wavelet transform of the next time scale is calculated; d is the result of the wavelet transform calculation; k is the time scale number; i is the signal point index.
As a result of wavelet transform of each cardiocycle at different time scales, a matrix of halfdifferences is obtained based on which the image is formed. This image then will be fed to the ANN input layer. A total of 6 time scales of transformation is used, an example is shown on Fig. 7.
At the moment, most researchers in signal, speech and image recognition algorithms use a neural
network [
To solve the problem of cardiocycle segments localization based on the wavelet transform results, the apparatus of convolutional ANN (which have been successfully used for image processing in recent years) was chosen.
The first convolutional ANN (which borrowed for computer science the ideas embodied by nature in
the visual cortex) was the ANN of Kunihiko Fukushima (Neocognitron, 1975-1980) [
The input data for the ANN in this paper are the Haar wavelet transform results performed on the average cardiocycle, presented in the form of images of size 200x6, where 200 – the number of counts constituting the cardiocycle (1 second), 6 – the number of time scales of the Haar wavelet transform.
The base of the cardiac cycle segments recognition system are the modules of the convolutional
The main modules of the proposed ANN structure are convolutional layers. To avoid the network overfitting problem to the ANN it is added the layers of random transmission shutoffs of the particular outputs (dropout) with a probability of outputs disconnection equal to 25%.
The last two layers of ANN are dense (fully connected) layers. A formed structure of the ANN outputs based on the requirements of the solved problem is following: an array of 200 outputs for each segment (P, QRS, T), i.e. total of 600 outputs.
To train the recognition system, it is necessary to form a correct training sample base. Each training example should include the following: the image obtained as a result of the Haar wavelet transform of the average cardiocycle, as well as the coordinates of the start and end indexes of the segments (P,
Before training the ANN, it was necessary to modify the training sample to bring the format of target responses for each training example in accordance with the ANN outputs. On the basis of a set of 6 coordinates of 3 segments from each cardiac cycle allocated by the cardiologist 3 array of outputs target values for each segment separately are formed according to the following formula (2): = 1, ∈ [ 0, 1 ], (2)
0, ∉ [ 0, 1 ] where i = {1...200} is the ANN’s output index and the coordinate on the average cardiac cycle; tmi is the target output value; m is the segment number; im0 and im1 is the indexes of the start and end of the segment marked by the expert.
After obtaining a set of outputs for each segment by using ANN it is necessary to interpret them. Each training example after transformation by formula (2) contain an image of the wavelet transform result of the average cardiocycle and an array of 600 values, the localization of each segment in which will be allocated units (Fig. 7).
The mean square error (MSE) is chosen as the optimization criterion in this work. The ANN’s output MSE is the difference between the desired result (target) and the actual output. In the process of ANN fitting the regression problem is solved, i.e. the values of all outputs obtained during the work of ANN should match with all target outputs values in the training sample. To measure the recognition quality we use the standard error function:
MSE = 1 ⋅ 1 ⋅ ∑ ∑ ( )2 = ∑ ∑ ( − )2, on the ANN’s current weights values and the input example); tmi is the target output value. where emi is the error value of the segment’s m output i; ymi is the output obtained by ANN (depends
The ANN learning process is reduced to correcting the ANN weights, so as to minimize the MSE.
The gradient descent method is generally used to minimize the MSE. In this work, an adaptive Adam
algorithm based on gradient descent with smoothed versions of the mean and standard gradients is
(3)
used to optimize MSE. [
Training samples base consisting of 1500 elements was used to fit the ANN. All samples were divided into training and test subsamples with the ratio of 80% by 20%, i.e. training subsample contains 1200 examples and the test subsample contains 300 examples.
The average period of the ANN’s training was 1 hour and 40 minutes on Lenovo G505s laptop (CPU AMD A10-5750M, RAM 4 GB). The graph of the error function obtained during ANN training is shown on Fig. 6, where the abscissa axis is the learning epoch number.
Training error displays the ANN’s fitting accuracy on a training subsample. However, it does not give a full confidence that the trained model will also be working well on a new data that was not in the training subsample. The model accuracy on the new data is the ANN generalizing ability. To estimate the model generalization ability, the generalization error obtained on the test subsample was used (Fig. 6).
The ANN learning process is iterative. Each iteration is called an epoch. During one epoch, all the examples from the training subsample are submitted to the ANN input. It is also possible to validate the fitting error on the test subsample. As can be seen on the charts, the error function reaches a minimum at epoch 19.
After the ANN training phase, it is possible to use the cardiac cycle segments recognition system on unknown signals. During operation, as well as during training, the wavelet Haar transform of the average cardiocycle is applied, and then the resulting image is fed to the ANN input. The ANN was localized precisely enough the P and QRS segments on the EGG signal which neither was in the training nor in the test subsample (Fig. 7). Segment T localization error could be the result of an inaccurate marking by the expert.
Figure 7. The example of segments localization results.
To perform experiments with the ECG morphology analysis system based on the proposed ANN,
the Keras library was used – an open-source ANN library written in Python. It is capable of running
on top of the Deeplearning4j, TensorFlow, or Theano frameworks. In this work, Keras was used along
with TensorFlow – an open-source software library for machine learning. [
The Table 1 is showing the results of practical comparison of the proposed cardiocycle segments
recognition system (based on convolutional ANN) and the previous version of recognition system
proposed in [
a) elimit is the absolute difference between manual marking and automatic recognition of a segment coordinate, the error expressed in counts;
According to the clinical requirements for the quality of the algorithms results for the cardiocycles segments localization on real signals, a maximum error of no more than 40 MS is allowed. In our case, when the quantization frequency is of 200 Hz, maximum allowable error is equal 8 counts.
According to these requirements, the recognition system based on ANN with a maximum allowable
error of 8 counts showed satisfactory results for the following segments (rows in table 1 marked are
grayed out): P – 82.18 % of samples, QRS – 88.74 % of samples, and T – 85.36 % of samples. The
system based on the pattern recognition proposed in [
The system based on convolutional ANN proposed in this paper showed results slightly superior to the
previous system based on pattern recognition [
The proposed system effectively solves the problem used the standard modules of modern convolutional ANN, which simplifies the development of signal and image analysis systems.
The obtained results should be considered as satisfactory given that the training sample was formed
mainly on the basis of the ECG from the functional diagnosis cardiological department with large
percentage of it were pathological ECG [
In the future researches it is possible to modify the developed ANN structure by adding new layers to ANN. It is also necessary to increase the variety and volume of training sample signals. Thus, it is possible to improve the recognition system and use it in a clinical practice.