Nonlinear model-based cardiac arrhythmia diagnosis using the optimization-based inverse problem solution

Abstract

This study investigates a nonlinear model-based feature extraction approach for the accurate classification of four types of heartbeats. The features are the morphological parameters of ECG signal derived from the nonlinear ECG model using an optimization-based inverse problem solution. In the model-based methods, high feature extraction time is a crucial issue. In order to reduce the feature extraction time, a new structure was employed in the optimization algorithms. Using the proposed structure has considerably increased the speed of feature extraction. In the following, the effectiveness of two types of optimization methods (genetic algorithm and particle swarm optimization) and the McSharry ECG model has been studied and compared in terms of speed and accuracy of diagnosis. In the classification section, the adaptive neuro-fuzzy inference system and fuzzy c-mean clustering methods, along with the principal component analysis data reduction method, have been utilized. The obtained results reveal that using an adaptive neuro-fuzzy inference system with data obtained from particle swarm optimization will have the shortest process time and the best diagnosis, with a mean accuracy of 99% and a mean sensitivity of 99.11%.

Introduction

Today, medical support systems play an important role in the accurate and rapid diagnosis of diseases. In the meantime, since heart disease has always been the leading cause of many deaths in humans, the use of medical support systems for the diagnosis of cardio-related diseases is cardinally important. Irregular heart rhythm (or cardiac arrhythmia) can signify heart disease. In fact, after determining the type of arrhythmias, the patient's condition can be determined by the electrocardiogram signal (ECG). Due to the diversity of arrhythmias and the time-consuming process of ECG signaling, there is always a possibility of human mistakes in the diagnostic process.

Automatic diagnosis of cardiovascular disease in medical and emergency cardiac patients can reduce the challenges of noise, artifacts, and human mistakes, leading to the improvement of medical standards in this area. Therefore, using soft processing techniques and machine learning in medical systems is important for cardiovascular diseases; many efforts have hitherto been made to develop methods for detecting arrhythmias from an ECG signal. To this objective, some researchers have focused on two aspects of ECG signal pre-processing: eliminating noise and artifacts and beat segmentation to improve the diagnosis of arrhythmias from the ECG signal [1–3]. Nonetheless, in many studies, the focus has been on two main aspects of work: features extracting and applying an effective classification method [4–8].

The features extraction is one of the most important parts of the work as it impacts the classification directly and significantly. Among the features used in the published papers, the features of the time/frequency domain [9, 10], wavelet transform [11–13], and morphological features [14, 15] are noteworthy. Research has shown that, due to the nonlinear and dynamic nature of ECG signals, using nonlinear methods is more efficient in extracting the features compared to linear methods. Hence, the development of nonlinear feature extraction methods to increase the accuracy of arrhythmias diagnosis appeals more to the interest of the researchers [16].

The model-based approach is an innovative nonlinear features extracting method [17]. In this approach, using a nonlinear dynamic model of ECG signal and an optimization-based inverse problem solution, parameters of the model are extracted as features when the ECG model output matches the real ECG signal. Extracting ECG signal features from the dynamic model is one of the nonlinear methods that can increase noise and artifacts detection robustness.

Optimization-based inverse problem solution methods are a critical field of applied mathematics and scientific computing, which have many applications in different areas of engineering and science. Generally, the inverse problem solution is understood as finding particular physical properties of the under investigation system, using indirect measurements [18]. Examples of the reverse solution method applications can be found in the field of medical imaging [19], cancer detection [20], fault detection [21], geography and exploration [22].

So far, much attention has been paid to producing synthetic ECG signals by mathematical models. Different models have been developed for the dynamic behavior of the ECG signal [23–27], the most important applications of which is to process and analyze the ECG signal [28, 29]. The most famous mathematical model presented for the ECG signal is the Zeeman model, presented in 1972 [30]. Because of the lack of attention to the biological parameters such as sympathetic and parasympathetic modulation, the new version of the ECG model was introduced later on [25, 31], the most notable work of which is the one by McSharry et al. in 2003, with the corresponding open-source model available on the Physionet website [25]. The McSharry model produces the ECG signal by solving three nonlinear equations that describe the dynamical description signal of the ECG. Some parameters of these equations alter the shape of the signals by changing them.

Choosing an effective classification method is another essential part of the work that can significantly affect the determination of the diagnosis accuracy. Some of the methods used to classify heart disease can be found in the following: artificial neural network (ANN) [32], support vector machining (SVM) [33], fuzzy c-mean clustering (FCM) [34], self-organizing map (SOM) [35], and optimum-path forest (OPF) [36]. Also, data reduction techniques [37] and feature selection [38] methods have been used in many works to enhance the efficiency of the methodology.

In the related literature, many studies have been done on the intelligent diagnosis of various arrhythmias from the ECG signal, which refers to some of the most important and recent works. In [39], Jovic et al. used the linear and nonlinear features of the heart rate variation (HRV) derived from the ECG signal for eight types of arrhythmias diagnosis. The study compared 56 linear and nonlinear features in eight combinations with three classifiers (including random forest, AdaBoosted C4.5, and SVM) to diagnose arrhythmias. The best performance was achieved by using a combination of nonlinear time domain features with random forest classification with an average accuracy of 85%.

Khalaf et al. employed the method of analyzing the cyclostationary signal, which has a robust behavior to noise, to extract and apply the spectral correlation coefficients of statistical and nonlinear features. Also, they implemented the method of reducing the dimensions of PCA and the Fisher score together with SVM's classifier in order to detect five types of rhythms. The final accuracy in detecting five rhythms (namely: normal rhythm, premature ventricular contraction (PVC), premature atrial contraction (PAC), left bundle branch block (LBBB), and right bundle branch block (RBBB) arrhythmias) was reported to be 98.6% [40]. Martis et al. used the higher-order statistics (HOS) method to retrieve nonlinear features based on the non-stationary and nonlinear nature of the heart. In this paper, the detection of five rhythms containing normal rhythm, right bundle branch block (RBBB), left bundle branch block (LBBB), premature atrial contraction (PAC), and ventricular premature contraction (VPC) has been investigated by using the least square-support vector machine (LS-SVM) classification techniques, along with the PCA1 data reduction method. The accuracy was found to be 93.48% [41]. Elhaj et al. tried to detect five types of non-ectopic beats, supra-ventricular ectopic beats, fusion beats, and unclassifiable and paced beats using nonlinear methods of independent component analysis, high order statistics, and cumulates, in combination with the linear technique of discrete wavelet transform coefficients. In this work, the SVM classification method with radial basis function has been used, the accuracy of which is estimated to be 98.91% [42].

The use of dynamic model parameters as a feature for diagnosing heart disease was first performed by Vafaie et al. [17]. In this work, by employing the McSharry model [31] and genetics algorithm, and using the model parameters as the features of ECG signal, the normal heartbeat, atrial fibrillation, ventricular tachycardia, and congestive heart failure was detected, and a genetic-fuzzy classifier analysis was performed. The accuracy of this diagnosis was reported to be 98.67%. One of the main challenges in extracting the parameters of the ECG model as a feature is the high extraction time of the parameters using the optimization method, which has not been addressed in reference [17].

As far as the scope of the paper is concerned, employing nonlinear model-based methods to extract the ECG signal features for the diagnosis of heart disease has been considered recently. In this paper, it has been tried to increase the diagnostic algorithm accuracy and reduce the extraction time of the model parameters. In this way, the diagnosis of arrhythmias of atrial fibrillation, ventricular tachycardia, congestive heart failure, and heart rate is studied. The main novelties of this work can be summarized as:

• In the feature extraction phase, a new structure is proposed to achieve a reliable and short time optimization-based inverse solution.

• With pre-processing conducted, only one heartbeat is segmented, and its features are obtained from the model. Also, the duration of the beats has been used as a model parameter, which reduces the optimization time and increases the diagnosis accuracy.

• A comprehensive comparative study has been performed on the optimization algorithm type and classification method to find the best results with the short time solution.

The organization of this paper is denoted as follows: Sect. 2 presents the database and data set description; Sect. 3 proposes methodologies. The utilized dynamic models, pre-processing methods, optimization methods, classifying methods, and the PCA data reduction method have been elaborated in this section. The main results are provided in Sect. 4. Section 5 presents the discussion. Finally, the conclusions are given in Sect. 6.

Methodology

Nonlinear dynamic model of ECG

Here, the McSharry model has been used to extract the features of ECG signals. Three differential equations of the model are:

$$\dot{x}=ax-\omega y$$ 1

$$\dot{y}=ay-\omega x$$ 2

$$\dot{z}=-\sum _{i\in [PQRST]}{\alpha }_i\mathrm{\Delta }{\theta }_{i}exp\left(-\frac{\mathrm{\Delta }{\theta }_i^2}{2b_{\partial }}\right)-(z-z_0)$$ 3

While:

$$\alpha =1-\sqrt{x^2+y^2}$$ 4

$$\mathrm{\Delta }\theta =\frac{(\theta -{\theta }_i)}{2\pi }$$ 5

$$\theta =\alpha tan(2\lambda )$$ 6

$$z_0=Asin(2\pi f_{2}t)$$ 7

In the above equation, $\theta$ is the quadrant arctangent of the real parts of $x$ and $y$, provided that:

$$-\pi \le \alpha tan2(x,y)\le \pi$$ 8

Also, the trajectory angular velocity is obtained from the duration of a beat. The coefficient of $A$ is a constant value, which determines the bias of the ECG, and $f_2$ is the breathing frequency. As can be seen, the ECG signal PQRST complex features are included in the equations by the parameters $a_i$,$b_i$, and ${\theta }_i$. The position of the waves is set by ${\theta }_i$, and their amplitude and width, are represented by $a_i$ and $b_i$, respectively. Solving Eqs. 1 to 3, an ECG signal mapping in a three-dimensional space is obtained on the circumference of a circle with a radius of one. The elements $x$ and $y$ define the coordinates on the circumference and the $z$ is the signal size. Some parts have been added to the modified model to include sympathetic and parasympathetic effects. In this regard, the low frequencies (LFs) Mayer wave, the high frequencies (HFs) sinus arrhythmia of respiratory, and the LF/HF ratio are added to the modified model. The modified model is fully described in [31].

To extract the characteristics of ECG signals, the McSharry model is used in the cost function structure of the optimization. The parameters in the equations are created through optimization algorithms. After solving the ECG signal equations, the created ECG signal is compared with the actual ECG signal, and the error value is calculated. The optimization process continues to find optimal parameters.

Pre-processing

In this paper, two approaches have been taken before the features are extracted by optimization. The first approach is based on the work done by Vafaei et al. [17], on which no pre-processing has been implemented. In this case, ECG signals with a length of three seconds are used for optimization. In order to reduce the optimization time in the second case, only the parameters of a beat are detected. Therefore, it is necessary to separate one beat from the signal. This is done using the R-peak detection method, and the number of beats per minute is obtained simultaneously [43]. Another attempt is made in the pre-processing phase by removing the bias from the ECG signals, which is not implemented in the first approach. This increases the time of matching the output of the model and the main signal in the optimization.

Feature extraction

The optimization method is used to extract the features of the ECG signals (namely, the parameters of the dynamic model). In this paper, two approaches have been used for this purpose. The first approach is similar to [17], and the second approach is the proposed method of this paper (Fig. 1). Considering that this study aims to reduce the optimization time and increase the accuracy of the arrhythmias diagnosis, various situations have been investigated to provide the best results.

Fig. 1.

a Feature extraction flowchart for the first approach, b feature extraction flowchart for the second approach includes two optimization methods for comparison

In the first approach, the extracted data (3-s long) directly enter the optimization to identify the dynamic model parameters, and the 15 parameters of the dynamic model are identified using the genetic algorithm. These 15 parameters are related to amplitude, width, and phase of PQRST ($[{\alpha }_i,b_i,{\theta }_i];i\in (P,Q,R,T,S)$).

The McSharry model has been used as the cost function of this approach (Fig. 1a). The cost value is the root of the mean square value of the difference between the dynamic model output and the actual ECG signal.

$$z=\sqrt{\frac{1}{N}\left(\sum _{i=1}^N{(S(i)-\widehat{S}(i))}^2\right)}$$ 9

In the above equation, N is the length (number of samples) of the ECG, S is the actual signal, and $\widehat{S}$ is the model output. Also,$z$ represents the cost amount that should be minimized through optimization.

In the second approach, pre-processing is performed. After signal offset removal, a single beat is segmented, and the heart rate is obtained in one minute. In this way, there will be no need for offsets and heartbeat rates during the optimization process. Two methods of GA and PSO have been used to realize the optimization effect. To decrease the optimization run time, a cascade structure is proposed. In this structure, by considering the amount of cost function and the number of iterations, it is decided whether the optimization is completed or it is necessary to change the search area bounds after each iteration. While, in the first approach, the optimization is completed after the maximum iteration is done (Fig. 1b).

The proposed cascade structure in the optimization is shown in Fig. 2. Parameters related to the cascade structure, such as the search area bounds, the optimal stopping cost, as well as the conditions for changing the search area bounds, are based on the observations made from the optimizations. Furthermore, both search area bounds are considered similar because of the high similarity of the normal and the AF signals.

Fig. 2.

Proposed cascade structure in the optimization flowchart

Genetic algorithm optimization

Genetic algorithm optimization is used to obtain the dynamic model parameters for ECG signals. In Table 1, the genetic algorithm parameters are given for the two implemented approaches. Given that the ECG signal does not necessarily require to correspond to the actual signal exactly, and knowing that decreasing the optimization time is very important, the population size and the number of generations are considered small, and the mutation and crossover coefficients are obtained by trial and error. The condition of optimization completion in the first approach is similar to [17] that is to reach the 30th generation, and in the second approach (by proposed cascade structure), it is to reach the 20th generation, or the break cost value condition is used for the end of optimization.

Table 1.

Optimization parameters for GA

Parameter	Value
	First approach [17]	Proposed approach
Population size	50	50
Generations	30	20
Variable numbers	15	15
Mutation	Uniform: 0.2	Uniform: 0.2
Crossover	Scattered:0.7	Scattered:0.7
Selecting	Stochastic uniform	Stochastic uniform

PSO algorithm

The particle swarm optimization (PSO) algorithm introduced by Kennedy et al. in 1995 is now one of the most well-known swarm intelligence optimization algorithms [44]. One of the obvious features of this optimization algorithm is its high speed to converge to the optimal solutions [45, 46]. Therefore, this optimization algorithm is also used to increase the extraction speed of dynamic model parameters. In this algorithm, particles move in search area bounds of parameters according to the global best position and best personal experience of each particle to achieve the best possible result. At each iteration, a new position and velocity for each particle are calculated according to the following equations:

$$v_i(t)=\chi \{v_i(t-1)+c_1{r}_1(lbes{t}_i-x_i(t-1))\}+\chi \{c_2{r}_2(gbes{t}_i-x_i(t-1))\}$$ 10

$$x_i(t)=x_i(t-1)+v_i(t)$$ 11

$$\chi =\frac{2}{\left|2-\phi -\sqrt{{\phi }^2-4\phi }\right|}$$ 12

In these equation $v_i$(t) and $x_i(t)$ are the velocity and position of particle $i$, respectively. $c_1$ and $c_2$ are learning factors, and $r_1$ and $r_2$ are random numbers in the range of (0,1). $lbes{t}_i$ and $gbes{t}_i$ are local best and global best, respectively. $\chi$ is the construction coefficient, which affects the convergence speed [47]. In this article $\phi$ is set to 4.1, and $c_1$, $c_2$ are set to 2.05. Other optimization parameters such as population size, iteration (or generation) and variable numbers, and also a condition of completion and cost function are considered as the proposed approach in Table 1.

Classification

Following the feature extraction based on the dynamic model of ECG signals, including 15 characteristics of amplitude, width, and phase, the components of PQRST complex and heart rate per minute (a total of 16 features), the classification methods can be used to diagnose diseases. In this paper, the fuzzy c-means (FCM) [48] and the adaptive neuro-fuzzy inference system (ANFIS) [49], along with the principal component analysis (PCA), have been used for classification. In [17], the fuzzy system and the fuzzy-GA system are used for this purpose but considering the very fact that all the data are used for training, the results are not reliable; while for evaluating the identification and classification methods, it is necessary to use a part of the data for test [50]. In the present work, the k-fold cross-validation method was used for training and validating the classification, considering k = 5. The k-fold cross-validation method is one of the highly valid techniques in training and validating the classifiers, eliminating concerns about the choice of test and training data sets, and providing accurate results [51].

Experimental results

Data set description

Providing reliable and suitable data to study the data-based methods is one of the main steps of this paper. Fortunately, the Physio Bank database has made it possible for researchers interested in working on heart disease [52]. Here, the required data are obtained from the MIT-BIH arrhythmia database. These data contain 48 half-hourly ECG labeled samples that include various types of arrhythmias. These data are recorded on two channels with a sampling rate of 360 samples per second and a resolution of 11 bits. The data of four types of rhythms are required for this work, including normal heartbeats (N), arrhythmias of atrial fibrillation (AF), congestive heart failure (CHF), and ventricular tachycardia arrhythmias (VT). From each rhythm, 75 signals with 3-s lengths are extracted. Atrial fibrillation is a prevalent atrioventricular arrhythmia due to the onset of a fast-electric pulse in the atria. This arrhythmia occurs when the irritation in the atrium is irregular and has no specific direction; that is, atria muscle cells are irregularly irritated [53].

Congestive heart failure is equivalent to reducing the ability of the heart to pump blood. People with heart failure often have a history of heart attacks in the past. Congestive failure may involve left or right, or both sides of the heart. Congestive heart failure often occurs in people over the age of 60, and more than 50% of people suffering from the disease die from heart attacks. Tachycardia or fast-paced heart rate increases to more than 100 beats per minute. In a person with ventricular tachycardia, a series of ventricular contractions originate from a point within the ventricles, and the heart rate exceeds 100 beats per minute. The main concern of this kind of cardiac tachycardia is that this kind of arrhythmia may cause problems with the regular blood pumpage by the heart, and the person may experience vertigo and syncope [53].

Feature extraction time

Some of the results are related to the optimization time of the features extraction; the computer used in this work is a PC with a CPU 2.40 GHz Intel® Core ™ i3 and 8.00 GB RAM. The results of the first approach optimization process are in accordance with the work of Vafaei et al. [17]; the optimization time for each data was 94 s, which is time-consuming. Using the proposed method in the structure of GA and PSO optimization algorithms significantly reduced the optimization time. As shown in Table 2, the time intervals were obtained in different scenarios.

Table 2.

The runtime of the optimizations in different states (s)

Optimization	Normal	AF	VT	CHF	Average
GA [17]	94	94	94	94	94
GA	21.27	14.45	42.65	37.08	28.85
PSO	19.93	16.43	36.45	31.36	26.04

The time results obtained from the optimization section for extracting the model parameters suggest that the shortest time corresponds to using the PSO optimization method.

Classification results

After extracting the model parameters for all the data, it is time for classification by these features. To evaluate the classification results, performance factors of accuracy, sensitivity, specificity, and positive predictive value have been calculated. After calculating the performance factors in each fold, their average is calculated for fivefold. The FCM and ANFIS methods, as well as the PCA method, have been used in classification. This work was based on the features extracted from three methods (including simple GA optimization [17] and two cases related to the second approach: GA & PSO in the proposed cascade structure). Using PCA, the optimal number of reductions in the data dimension is obtained from trial and error. The results of using the FCM and PCA are illustrated in Table 3. The best results were obtained when the data dimension was reduced to 12 using PCA, and the number of Takagi–Sugeno fuzzy rules was considered to be four. This table presents the average values of each of the four performance factors for fivefold in the test phase. Accordingly, the best results are obtained using parameters derived from the PSO method. Using ANFIS and PCA methods for classification yielded better results compared to the FCM; the best results were obtained by reducing the data dimensions to five and selecting two Gaussian type membership functions for each input and 500 iterations in the training phase. The best answers with very little difference are achieved in these situations when the PSO features are used. Table 4 shows the average performance factors for fivefold in the test phase for each condition.

Table 3.

Average FCM-PCA classification results over fivefold in the test phase

Performance	Simple GA [17]	proposed method and GA	proposed method and PSO
Average accuracy (%)	94	94.33	96.67
Average sensitivity (%)	95.11	93.78	96
Average specificity (%)	90.67	96	98.67
Average PPV (%)	96.76	98.60	99.52

Table 4.

Average ANFIS-PCA classification results over fivefold in test phase

Performance	Simple GA [17]	proposed method and GA	proposed method and PSO
Average accuracy (%)	97	98.67	99
Average sensitivity (%)	96	98.67	99.11
Average specificity (%)	100	98.67	98.67
Average PPV (%)	100	99.56	99.56

Also, the results indicate that by employing the features obtained in a shorter time from the proposed optimization structure, the detection accuracy becomes higher than the first approach (simple GA optimization). The results of the proposed method, which include GA and PSO in the training and testing phases, are shown in Table 5, 6, 7 and 8 and Figs. 3, 4, 5 and 6. In Table 5, the details of the results of the FCM-PCA classification are presented in an average of fivefold in the train and test phase using the data obtained from GA. The existence of decimal numbers in Table 5 was due to the average number of detections in fivefold. In Fig. 3, the results are presented in the box plot diagram. The results of Table 5 and Fig. 3 show that the highest error occurs in diagnosing healthy rhythm and AF arrhythmia. Table 6 and Fig. 4 demonstrate the details of the results derived from the PSO data and the FCM-PCA method. In this case, the diagnosis of CHF in the training and testing phase was 100% accurate, and the most commonly mistaken diagnosis was for AF that was detected as normal. Better performance is achieved using the ANFIS and PCA methods, as shown in Table 7 and Fig. 5. As can be seen, using the data obtained from GA in detecting VT and CHF, the error rate is zero, and the largest error occurs in the diagnosis of AF arrhythmia. Table 8 and Fig. 6 show the detailed results obtained by the PSO data and implementing the ANFIS-PCA method, which brought the best results. In this case, the accuracy of the diagnosis of AF arrhythmia is also improved. As previously shown in Table 4, in this case, the highest accuracy and sensitivity are encountered within the diagnosis.

Table 5.

Average FCM-PCA classification results over fivefold (features extracted by the GA)

ECG groups with 60 samples for train and 15 samples for test	Train				Test
	The average number of ECG signals placed in each group over fivefold				The average number of ECG signals placed in each group over fivefold
	Normal	AF	VT	CHF	Normal	AF	VT	CHF
Normal	58.4	1.6	0	0	14.4	0.6	0	0
AF	4.4	55.6	0	0	1.4	13.6	0	0
VT	0	0	58	2	0	0.4	13.6	1
CHF	0	0	0	60	0	0	0	15

Table 6.

Average FCM-PCA classification results over fivefold (features extracted by PSO)

ECG groups with 60 samples for train and 15 samples for test	Train				Test
	The average number of ECG signals placed in each group over fivefold				The average number of ECG signals placed in each group over fivefold
	Normal	AF	VT	CHF	Normal	AF	VT	CHF
Normal	60	0	0	0	14.6	0.4	0	0
AF	5	54.4	0.6	0	1.4	13.6	0	0
VT	0	1.4	58.6	0	0	0.4	14.6	0
CHF	0	0	0	60	0	0	0	15

Table 7.

Average ANFIS-PCA classification results over fivefold (features extracted by the GA)

ECG groups with 60 samples for train and 15 samples for test	Train				Test
	The average number of ECG signals placed in each group over fivefold				The average number of ECG signals placed in each group over fivefold
	Normal	AF	VT	CHF	Normal	AF	VT	CHF
Normal	59.2	0.8	0	0	14.8	0.2	0	0
AF	1.6	58.4	0	0	0.6	14.4	0	0
VT	0	0	60	0	0	0	15	0
CHF	0	0	0	60	0	0	0	15

Table 8.

Average ANFIS-PCA classification results over fivefold (features extracted by PSO)

ECG groups with 60 samples for train and 15 samples for test	Train				Test
	The average number of ECG signals placed in each group over fivefold				The average number of ECG signals placed in each group over fivefold
	Normal	AF	VT	CHF	Normal	AF	VT	CHF
Normal	59.8	0.2	0	0	14.8	0.2	0	0
AF	0.8	59.2	0	0	0.2	14.8	0	0
VT	0	0.8	59.2	0	0	0.2	14.8	0
CHF	0	0	0	60	0	0	0	15

Fig. 3.

FCM-PCA classification results over fivefold in a training and b testing phases (features extracted by GA)

Fig. 4.

FCM-PCA classification results over fivefold in a training and b testing phases (features extracted by PSO)

Fig. 5.

ANFIS-PCA classification results over fivefold in a training and b testing phases (features extracted by GA)

Fig. 6.

ANFIS-PCA classification results over fivefold in a training and b testing phases (features extracted by PSO)

Discussion

In the current study, a model-based approach was applied to diagnose heart arrhythmias, AF, VT, and CHF via a normal ECG signal. The positive feature of the model-based method is its precision, and the time to extract the model parameters using the optimization method is the most critical challenge. In this study, it has been demonstrated that using some techniques makes it possible to achieve high accuracy and lower the detection time. In this regard, a cascade structure was used for optimization. GA and PSO optimization methods were implemented, and the McSharry model was used in the cost function. The results showed that using the PSO optimization algorithm and the McSharry model, the parameters of the ECG signal model were extracted in the shortest frame of time. Using the two methods of FCM and ANFIS together with the PCA technique in the classification section showed that the ANFIS method, using data obtained from PSO, has the highest performance with an accuracy of 99% and sensitivity of 99.11%.

The first and only work done to diagnose heart disease is based on the ECG dynamic model in [17]. In this work, the accuracy of the diagnosis was reported to be 98.67% using the fuzzy-GA classification. However, as noted earlier, the precision is not reliable due to the lack of classification validation in this work (the lack of test data). In order to verify the results more precisely, the model parameters were extracted from the data to obtain the optimization time and investigate the classification results according to the method used in [16]. The accuracy of 97% and sensitivity of 96% were achieved using ANFIS along with PCA and the cross-validation method.

It is assumed that pre-processing and segmentation of a single heartbeat to obtain parameters, as well as using the beat duration, have a great effect on reducing the optimization time, and using the heartbeat duration as a feature in the classification also improves the classification accuracy.

Conclusions

In the current study, the model-based method was used to detect three types of heart diseases: AF, VT, and CHF, and a healthy heart rhythm. For this purpose, after the beat segmentation, two GA and PSO optimization methods were used in a proposed structure to extract the ECG signal parameters. Using the proposed structure in optimization in its most optimal case reduced the extraction time of the model parameters by 3.6 times. ANFIS and FCM methods were used for classification. Therefore, the best results were obtained: 99% accuracy, 99.1% sensitivity, 98.68% specificity, and 99.56% PPV, which were the results of using the ANFIS method along with PCA through the data obtained from PSO. The results indicate the high ability of nonlinear model-based methods to extract the discrimination features of heartbeats types. According to the authors, using real-time programming languages, vectorization techniques in optimization, and parallel processing techniques effectively improve the time factor in model-based methods. They can be investigated by those interested in these fields.