Ischemia detection by electrocardiogram in wavelet domain using entropy measure.  
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BACKGROUND: Ischemic heart disease is one of the common fatal diseases in advanced countries. Because signal perturbation in healthy people is less than signal perturbation in patients, entropy measure can be used as an appropriate feature for ischemia detection. METHODS: Four entropybased methods comprising of using electrocardiogram (ECG) signal directly, wavelet subbands of ECG signals, extracted ST segments and reconstructed signal from timefrequency feature of ST segments in wavelet domain were investigated to distinguish between ECG signal of healthy individuals and patients. We used exercise treadmill test as a gold standard, with a sample of 40 patients who had ischemic signs based on initial diagnosis of medical practitioner. RESULTS: The suggested technique in wavelet domain resulted in the highest discrepancy between healthy individuals and patients in comparison to other methods. Specificity and sensitivity of this method were 95% and 94% respectively. CONCLUSIONS: The method based on wavelet subbands outperformed the others. 
Authors:

Hossein Rabbani; Mohammad Parsa Mahjoob; Eiman Farahabadi; Amin Farahabadi; Alireza Mehri Dehnavi 
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Type: Journal Article 
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Title: Journal of research in medical sciences : the official journal of Isfahan University of Medical Sciences Volume: 16 ISSN: 17357136 ISO Abbreviation: J Res Med Sci Publication Date: 2011 Nov 
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Created Date: 20120913 Completed Date: 20121002 Revised Date: 20130530 
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Nlm Unique ID: 101235599 Medline TA: J Res Med Sci Country: Iran 
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Languages: eng Pagination: 147382 Citation Subset:  
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Assistant Professor, Biomedical Engineering Department, Medical Image and Signal Processing Research Center, Isfahan University of Medical Sciences, Isfahan, Iran. 
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Journal Information Journal ID (nlmta): J Res Med Sci Journal ID (isoabbrev): J Res Med Sci Journal ID (publisherid): JRMS ISSN: 17351995 ISSN: 17357136 Publisher: Medknow Publications & Media Pvt Ltd, India 
Article Information Copyright: © Journal of Research in Medical Sciences openaccess: Received Day: 07 Month: 1 Year: 2011 Accepted Day: 02 Month: 9 Year: 2011 Print publication date: Month: 11 Year: 2011 Volume: 16 Issue: 11 First Page: 1473 Last Page: 1482 ID: 3430066 PubMed Id: 22973350 Publisher Id: JRMS161473 
Ischemia detection by electrocardiogram in wavelet domain using entropy measure  
Hossein Rabbani1  
Mohammad Parsa Mahjoob2  
Eiman Farahabadi3  
Amin Farahabadi3  
Alireza Mehri Dehnavi4  
1 Assistant Professor, Biomedical Engineering Department, Medical Image and Signal Processing Research Center, Isfahan University of Medical Sciences, Isfahan, Iran. 

2 Associate Professor, School of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran. 

3 Biomedical Engineering Department, Medical Image and Signal Processing Research Center, Isfahan University of Medical Sciences, Isfahan, Iran. 

4 Associate Professor, Biomedical Engineering Department, Medical Image and Signal Processing Research Center, Isfahan University of Medical Sciences, Isfahan, Iran. 

Correspondence:
Corresponding author: Hossein Rabbani Email: h_rabbani@med.mui.ac.ir 
Ischemia means lack of oxygen due to insufficient blood circulation. Ischemic heart disease is a condition with different causes which have one thing in common, the imbalance between the supply and demand of oxygen. This disease is one of the common fatal diseases in advanced countries.^{1} Arteriosclerosis, which is a general phrase for thickening and hardening of artery wall, is one of the main reasons of mortality in most countries.^{1} For epicardial coronary artery, it is the common cause of myocardial ischemia.^{2} More precisely, in more than 90% of cases, ischemia is due to atherosclerosis.^{3} Atherosclerosis is one type of arteriosclerosis that is developed in larger arteries and causes most cases of coronary artery disease, aortic aneurysm and arterial diseases of inferior limbs and it has an important role in cerebrovascular disease.^{4}–^{5} In addition, ischemia leads to certain changes of electrocardiography (ECG) signal such as electrical instability that may lead to ventricular tachycardia/fibrillation, and repolarization abnormalities identified by reversing T wave and displacing ST segment.^{6}–^{8}
Analysis of ECG signal has some problems such as lack of accurate and detailed information about cardiac electrical activity in all its levels and also lack of timely representation of information in critical and fatal diseases such as ischemia. However, it is widely used due to some advantages such as low cost and availability in all medical centers.^{9} There are different methods for automatic finding of ischemic states using ECG signal including waveletbased methods and timefrequency analysis,^{10}–^{16} techniques that are based on neural networks^{17}–^{19} and fuzzy systems,^{20} methods using principal component analysis^{21} and HMMbased techniques (hidden Markov model).^{22} Although these methods have some advantages, they also have disadvantages such as the long time required and complexity in neural network learning or high sensitivity to noise and not timely diagnosis in some timefrequency analysis methods.
In this study, the existence of ischemia is investigated using entropy measure.^{23} For this reason, 4 techniques in spatial and wavelet domains were considered to determine the optimal method having highest discrepancy between healthy subjects and patients. These methods were entropy analysis of ECG signal, entropy analysis of ECG signal in wavelet domain, entropy analysis of ST segments extracted from ECG signal, and entropy analysis of reconstructed signal using timefrequency features of ST segment in wavelet domain. The main contribution of this paper is finding a measure based on spatiotemporal analysis of ECG to determine the irregularity of ST segments. In the previous works, only some criteria such as entropy in signal domain were measured while in this study, after automatically extraction of ST segments, we tried to benefit from the advantage of spatiotemporal analysis of ECG signal to be able to calculate the irregularity of ST segments more precisely.
In this study a sample of 40 patients with meanage of 55 ± 3 years (24 men) who had ischemic signs based on initial diagnosis of a medical practitioner (such as chest pain^{24}) were selected. Finally, a the cardiologist evaluated and confirmed the results. We recorded ECG signals of patients at rest using 12lead Cardiax^{25} with sampling frequency of 500 (Figure 1) and ST deviation of 0.5 mm or variations of Twave proposed as ischemic signs. For each signal, 10 beats were analyzed using entropy measures in order to predict who would be stresstest positive without having to undergo an exercise treadmill test (as the gold standard). To be able to evaluate these methods, exercise treadmill test was performed for all subjects that resulted in 22 cases (out of 40) with positive stresstest.
Since the entropy measure is a criterion to measure the irregularity, it can be used as a feature for distinguishing between ischemic patients (people with positive stress test) and healthy (people with negative stress test) without having to undergo a stress test. Figure 2 shows a sample ECG signal (one lead) of a patient and a healthy person. Entropy is one of the main measures used in information theory.^{26} It is used for measuring uncertainty in random variables. The highest uncertainty indicates the highest amount of information. The entropy of a discrete variable X with probability density function P_{x}(x) is defined as follows:
H(X”) = –Σ_{x∈}P_{x}(X”) LogP_{x}(X”) (1)
H(x) is maximized when all occurrence of an experiment have the same probability (uniform distribution) and is zero when probability of one occurrence is explicitly one (delta distribution).
Since ischemic signals have more perturbations and are more chaotic in comparison to nonischemic signals, entropy can be used as a measure for classifying ischemic and nonischemic patients. The entropy has been usefully applied, for example, in analyzing variation in RR interval sequences.^{27}–^{34} However, we do not know whether it can also be applied to morphologic variation across a set of ST segments extracted from sequential beats. To justify the connection between the concept of entropy as a measure of uncertainty used in information theory and its use as a measure for classifying ischemic and nonischemic patients we used goodness of fit test.^{35} While the goodness of fit value for patients was 541.57 ± 36.28, it was 882 ± 41.54 for healthy subjects illustrates the difference between uniform distribution and histogram of ECG signals of patients and healthy persons using chisquare test.^{36} It shows that there was a significantly different degree of random variability in ischemic populations as opposed to nonischemic ones, and that the probability distribution was more uniform in one group than the other.
In this study four states were proposed for calculation of the entropy in order to obtain the state with highest discrepancy in entropy of healthy and patient subjects. These four states included:
In the first part, merely analyzing ECG signal of subjects in time domain is proposed. For this reason, entropy measure of all data is calculated. General structure of this part is as follows:
 1 Entropy measures for each lead of ECG signal are measured individually. For each signal 10 beats are analyzed using the first (1) equation.
 2 The average of obtained values in previous step for 12 leads is considered as total entropy of each person.
 3 The obtained value in previous step is compared to a threshold. If it is more/less than the threshold we consider this case as patient/healthy person.
The principle of discrete wavelet transformation (DWT) is related to subband coding originally introduced in 1976.^{37} To apply DWT, at first the signal is passed through a half band low pass digital filter with pulse response h[n]. Therefore, the frequency components higher than half of the highest frequency of signal are removed due to this filtering. Since the highest frequency in filter output is π/2, thus the length of signal would be halved by removing samples alternatively without losing any information. A similar procedure is performed with a half band high pass digital filter g[n]. Hence, in first step output of DWT are two “low pass” and “high pass” signals with decreased length (half) of original signal as follows:
Y_{high}[k] = Σ_{n}X[n]g[2k – n] (2)
Y_{low}[k] = Σ_{n}X[n]h[2k – n] (3)
Consequently, in this stage a time resolution is halved while frequency resolution is doubled. This procedure can be applied again on low pass subband and in each step, frequency resolution is doubled by halving time resolution. Generally, increasing level of entropy is due to the increasing perturbation in respective area, and this increases the probability of ischemia existence in respective area.
In this part, to obtain the entropy measure, the ECG signals are transformed to DWT domain and other operations are performed on produced signals from appropriate subbands in this domain. The main reason of using DWT is its power for separation of various timefrequency components in its subbands. Accordingly, DWT is an appropriate tool for distinguishing between unnecessary components (such as noise) from signal. After applying DWT on signal (performed in 4 levels and using Daubechies wavelet 4^{37}), it is required to use one of the produced signals from appropriate subbands as a reference in order to perform other processing operations on this signal.^{13} In this paper, according to figure 3, the reconstructed signal merely using subbands of last stage is named “Approximate 1”. “Approximate 2” is obtained by incorporating details of subband of previous stage for reconstruction, and consequently “Approximate 3” and “Approximate 4” are acquired using details of subbands of previous stages. The entropy is evaluated for these produced signals. The signal with higher entropy in patient subjects (indicating more perturbation) and the signal with lower entropy in healthy subjects (indicating less perturbation) are selected based on this fact that signal perturbation in healthy people is less than signal perturbation in patients.
The main steps of proposed method in this section can be described as follows:
 1 To apply DWT to ECG signal for each lead
 2 To calculate the entropy of “Approximate 2” for each lead.
 3 To average out the obtained entropy measures from leads.
The signal with average entropy higher than a threshold is defined as ischemic case based on this fact that signal perturbation in healthy people is less than signal perturbation in patients.
In this section, entropy measurement is performed with respect to ST segments extracted from ECG signals of patients and healthy subjects in order to achieve more accurate analysis of entropy. For this reason, ST segments are extracted for each lead (for each signal 10 beats are proposed) and their entropy measures are averaged (over all segments) to obtain the mean entropy for each case.
The first step in ST segment extraction is extraction of R wave. In this study adaptive threshold limit algorithm^{38} was used for R peak detection. It is designed using a pair of threshold limits called “up limited threshold (ULT)” (Eq. 4) and “down limited threshold (DLT)” (Eq. 5). If the numbers of peaks detected by ULT and DLT in each threshold step are not equal, error component is calculated and subtracted from limits and new thresholds are obtained. This repetition continues until these two limits equal and at last final threshold limit is specified.
TH_{m+1} = TH_{m} – W_{m}Δ (4)
TH_{f+1} = TH_{f} – W_{f}Δ (5)
In above equations TH_{m+1} and TH_{f+1} are modified threshold limit values, TH_{m} and TH_{f} are initial threshold limit values, and Δ = TH_{f} – TH_{m} is the difference between two determined limits. W_{f} and W_{m} are error weight factor which in each step have specific value with respect to number of false detected peaks. J point detection is done after specifying R point in desired signals. Thus, after detection of these two points (points related to R wave and J point) extraction of ST segment can be performed.^{9} In this respect, after extraction of J point, 80 and 120 milliseconds after that is considered (respectively for healthy people and tachycardia patients) as the end of component (or start of T wave).^{39}Figure 4 shows a comparison between the ST segments of a patient and healthy people.
According to our explanation in this section, the proposed method is a refinement of the first method and analyzes just the ST segment of the timedomain waveform rather than the entire beat. The main steps of proposed method can be described as follows:
 1 Extract the ST segment of 10 beats of ECG signal of each lead.
 2 Measure the entropy of extracted signal in previous step using (1).
 3 Calculate the average of obtained values in previous step for all 12 leads in order to obtain the total entropy of each person.
 4 The obtained value in previous step is compared to a threshold. If it is more/less than the threshold we consider this case as patient/healthy person.
In this section, in order to more accurate analysis of ECG signal, after transforming signal to wavelet domain, since ST segment frequency is about 3040 Hz, second subband including 3060 Hz frequencies is selected as reference subband.^{13} Then ECG signal is reconstructed using only filtered version of this subband. After signal reconstruction, entropy measure related to this signal is measured and a comparison is done between data of healthy and patient subjects. The proposed method in this section is a refinement of the second method and uses a waveletfiltered version of the original waveforms to accentuate the ST feature. The main steps of proposed method can be described as follows:
 1 To apply DWT to ECG signal for each lead
 2 To reconstruct the signal using (only) filtered version of the second subband
 3 To calculate the entropy of reconstructed signal in previous step for each lead
 4 To average out the obtained entropy measures from leads
The signal with average entropy higher than a threshold is selected as ischemic case based on this fact that signal perturbation in healthy people is less than signal perturbation in patients. Figure 5 illustrates a sample of reconstructed signal for a patient and a healthy person. Note that we can produce more appropriate signals according to timefrequency properties of ST segment using wavelet packet.
We used a gold standard of the exercise treadmill test, with a sample of 22 patients who were stresstest positive and 18 who were normal. The goal was to predict who would be positive without having to undergo a stress test. Table 1 shows entropy measures obtained using proposed methods in this paper for both patients and healthy people. As it can be observed from the obtained results in table 1, discrepancy between obtained components from ECG signals was less than results obtained from extracted subbands. In addition, in ST segments extracted from signals and reconstructed signal from timefrequency properties of ST segments in wavelet domain, the average entropy obtained from healthy subjects was less than patients. Considering different states among all patients of the study, it was observed that discrepancy between components obtained with respect to first (ECG signal analysis), third (ST segments analysis) and fourth (analysis of reconstructed signal from time frequency features of ST segment in DWT domain) methods was less than results obtained from subbands of wavelet (second method). For methods 1 to 4, the correlation with stress test was 75, 95, 67.5 and 50, respectively. These correlation coefficients confirm this outcome by comparing the correlations between results of stress test and proposed methods in this paper for ischemia detection.
According to these findings, it can be observed that entropy measurement for above groups suggests that since perturbation in patient's signals with positive stress test was more than subjects with negative stress test (due to existence of irregular ST segments and/or QRS complexes), obtained entropy measures had higher levels. As it can be seen in table 1, the highest discrepancy occurred in second method (entropy analysis of ECG signal in wavelet domain) and thus this method is the optimal one for ischemia diagnosis. Table 2 shows the sensitivity and specificity of all methods used in this paper. Comparing the results of this table with table 3 which shows the results of other methods introduced in other studies,^{23}^{, 40}–^{43} we can conclude that our methods outperformed previous techniques.
In this paper the entropy measure is proposed as a feature for ischemia detection in order to estimate significant STsegment deviation in exercise test. For this reason, entropy was measured using four manners, i.e. using ECG signal directly, using wavelet subbands of ECG signals, using extracted ST segments, and using reconstructed signal from timefrequency feature of ST segments in wavelet domain. Our simulations showed that proposed method based on wavelet subbands outperformed the others.
In this study we only used Daubechies wavelets. Using other transforms such as undecimated wavelet and complex wavelet^{44} (that have shift invariant property) or wavelet packet (that is able to better specify timefrequency properties of ST segments) could improve the results. In addition, a similar entropybased manner can be used for detection of other heart diseases such as myocardial infarction (MI). Moreover, we used stresstest as a gold standard. It is clear that stresstest may result in incorrect results and better evaluation could be achieved using angiography as a gold standard.
EF and AF participated in most of the experiments and carried out all the experiments. HR carried out the design and coordinated the study and prepared the manuscript. AMD provide assistance in the design of the study and participated in manuscript preparation. MPM provided assistance for all experiments. All authors read and approved the content of the manuscript.
Notes
Conflict of Interests Authors have no conflict of interests.
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Keywords: KEYWORDS Ischemia, Electrocardiogram, Exercise Test. 
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