Enda Moloney 05367981 B.E. Electronic Engineering Project Report EE426
Classification of Electrocardiogram (ECG) Waveforms for the Detection of Cardiac Problem P roblemss
March 2009
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Abstract
The primary aim of this project is to design a computer-based system for the processing and classification of Electrocardiogram waveforms with the intention of assisting in the detection of abnormalities and therefore facilitate the early detection of cardiac problems. Important features of the ECG waveform such as the timing of significant events are obtained. Individual waveforms are examined. The PanTompkins algorithm and the Fourier Transform for the ECG signals are discussed. There is a review of Artificial Neural Network (ANN) and how it can be applied to ECG data. The report concludes with a summary of results and suggestions for future work.
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Acknowledgements
I would like to thank Dr. Edward Jones for all his help, guidance and assistance in this project throughout the year. I would like to also thank my family for all their help and encouragement during the last four years.
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Declaration of Originality
I declare that my thesis is original work except where otherwise stated. Signature:
Data:
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Table of contents Abstract..................................................................................................................... 2 Acknowledgements ................................................................................................... 3 Declaration of Originality .......................................................................................... 4 Table of contents ....................................................................................................... 5 1.0 Introduction ......................................................................................................... 6 2.0 Physiological Background ................................................................................... 8 2.1 The Heart and ECG waveform ............................................................................. 8 2.2 History of ECG.................................................................................................. 10 2.3 ECG signals ....................................................................................................... 12 3.0 System Overview .............................................................................................. 15 3.1 From signals to samples ..................................................................................... 15 3.2 MIT-BIT Database ............................................................................................ 16 4.0 QRS Detection................................................................................................... 19 4.1 Introduction ....................................................................................................... 19 4.2 Pan-Tompkins algorithm ................................................................................... 20 4.3 Finding the QRS peaks ...................................................................................... 23 4.4 Getting individual beats ..................................................................................... 24 4.5 Exact times of the QRS complex ....................................................................... 25 5.0 Fourier Analysis ................................................................................................ 26 5.1 Fourier Transform ............................................................................................. 26 5.2 Fast Fourier Transform ...................................................................................... 27 5.3 Implementation of the Fourier Transform .......................................................... 29 6.0 Artificial Neural Network .................................................................................. 32 6.1 ANN as applied to ECG signals ......................................................................... 32 7.0 Results and Conclusion ...................................................................................... 35 8.0 References ......................................................................................................... 42 8.1 Bibliography...................................................................................................... 43 9.0 Appendix ........................................................................................................... 44
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1.0 Introduction
The primary aim of this project is to design a computer-based system for the processing and classification of Electrocardiogram waveforms with the intention of assisting in the detection of abnormalities and hence facilitating early detection of cardiac problems. Cardiac arrhythmias are malfunctions of the heart, which if left untreated could result in serious health problems. The project uses software called MATLAB programming language; this detects and diagnoses problems. Such a system would not be intended to replace a human cardiac specialist; rather it would be intended to “flag” patients with potential heart problems, thus enabling early referral to a specialist. A goal of the project is to compare a number of approaches to the problem, based on criteria such as performance as well as computational complexity. For development purposes, the MIT-BIH database of ECG waveforms and corresponding annotations can be used for test data. All problems associated with each wave have already been identified in the MIT-BIH database. The Fast Fourier Transform is applied to these ECG waves to extract information about them and using Artificial Neural Network they are divided into different classes. Information about the duration of the QRS complex was extracted from the ECG wave; this can be used to detect abnormalities. This report is presented in a number of chapters as follows: Chapter 2 gives an explanation of the working of the heart and the various features of the ECG signals. Chapter 3 reviews the algorithm used in the project. Chapter 4 discusses QRS detection and the Pan-Tompkins algorithm. Chapter 5 reviews the Fourier Transform
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and how it can be applied to the ECG signal. Chapter 6 reviews the uses of Artificial Neural Network as applied to ECG signals. The concluding chapter presents results and conclusions with suggestions for future work. At the end of the report there are references, bibliography and an appendix.
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2.0 Physiological Background This chapter reviews the working of the heart and how it produces ECG waves. The history of measurement of an ECG signal is explained. The characteristic features of an ECG signal are outlined.
2.1 The Heart and ECG waveform The heartbeat is started by a „pacemaker‟ called the sinoatrial node (SA node) as shown in Fig 2.1. It is situated in the right atrium near the point where the venae cavae enter. This node is a specialised area of heart muscle that generates electrical impulses. The electrical impulse travels to the atrioventicular (AV) node. Here there is a very brief delay to allow atria to contract. From the AV node the electrical impulse spreads into Purkinje fibres causing ventricles to contract. This complete cardiac cycle takes place about 70 times in one minute. Each cycle takes about 0.8 of a second. An electrocardiogram (ECG) is a recording of the electrical activity of the heart as electrical signal spreads from the right atrium to the left atrium.
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Figure 2.1: Heart
.The ECG is a recording of the electrical activity at a fixed rate and a graph is plotted of voltage on y-axis against time on the x-axis.
There are a wide variety of uses for ECG such as:
Determining if the heart is performing normally or suffering from abnormalities such as extra or skipped heartbeats.
Indicating previous damage to the heart muscle.
Providing information on the physical condition of the heart.
Been used to detect non-cardiac diseases (e.g. Pulmonary embolism, hypothermia).
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2.2 History of ECG
In the nineteenth century it was difficult to measure the electrical signal for the heart; moving coil galvanometers were not sensitive enough to measure the tiny electric currents. A breakthrough came in 1901 when Einthoven invented the string galvanometer. [1] This device was more sensitive than the capillary electrometer that Waller used and the string galvanometer that had been invented separately in 1897 by the French engineer, Ader. The electrical activity of heart can be measured by an array of electrodes placed on the body. The recorded tracing is called ECG. The different waves represent the sequence of contraction and relaxation of the atria and ventrials. [2] ECG is recorded at a speed of 25mm/sec and voltage is calibrated so that 1mV = 10mm in the vertical direction. Therefore each small 1mm square in figure 1 represents 0.04 sec in time and 0.1mV in voltage, as shown in fig. 2.2
Figure 2.2: A "typical" ECG tracing
Einthoven assigned the letters P, Q, R, S and T to the various deflections, and described the electrocardiographic features of a number of cardiovascular disorders.
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The meaning of these letters is discussed in more details later. In 1924 he was awarded the Nobel Prize in Medicine for his discovery. Though the basic principles of that era are still in use today, there have been many advances in electrocardiography over the years. The instrumentation, for example, has evolved from a cumbersome laboratory apparatus to compact electronic systems that often include computerized interpretation of the electrocardiogram. Einthoven‟s string galvanometer is known as Einthoven‟s triangle because three leads were used which were literally placed on the arms and legs in buckets of salt water in order to obtain a electrical signal. Electrodes were later invented which could be place directly on the patient ‟s skin and they are still placed on the arms and legs. They are the first three leads of the now twelve leads that are used in the modern ECG., as shows in fig. 2.3.
Fig 2.3: Placement of the leads on limbs
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A lead 1 is a dipole negative electrode (white) on the RA and positive (black) electrode on LA. Lead 2 is a dipole with negative electrode (white) on RA and positive (red) electrode on LL. Lead 3 is dipole with negative (black) electrode on LA and positive (red) on LL
2.3 ECG signals An ECG is constructed by measuring the electrical potential between various points of the body using leads. The normal ECG wave is composed of 1. The P wave 2. QRS complex 3. ST segment 4. The T wave 5. U wave The relationship between P waves and QRS complexes helps distinguish various cardiac irregularities. Below is a computer generated image of a healthy ECG trace.
Fig 2.4: Representation of ECG wave
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P wave The P wave is formed as a result of the spread of electrical signal through the muscles of the atrium; this causes the atrium to contract. The P wave is normal between 0.08 to 0.1 seconds (80-100ms) in duration. During normal atrial contraction, the main electrical vector travels from the Sinoatrial (SA) node towards the Atrioventricular (AV) node, and spreads from the right atrium to the left atrium. This turns into the P wave on the ECG. The shape and duration of the P waves may indicate atrial enlargement. The brief period after the P wave represents the time in which the impulse is travelling within the AV node. In the AV node the speed of the electric signal is greatly reduced. The period of time onset of the P wave to the beginning of the QRS complex is termed the P-R interval. The normally is 0.12 to 0.2 second duration. P-R interval is the time between the contraction of the atria and the contraction of the ventricles. If the P-R interval is more that 0.2 of second this indicates serious problems with the heart
QRS complex The QRS represents the spread of the electrical impulse through t he muscle of the ventricles. The QRS complex is a structure on the ECG that corresponds to the depolarization (contraction) of the ventricles. The muscles of the ventricles are bigger than the muscles of the atria: this means QRS complex is larger than the P wave. The QRS complex is normally between 0.06 and 0.1 second; this is a very short period of time and shows that Ventricular depolarization occurs very rapidly. The duration and amplitude of the QRS complex is useful in diagnosing cardiac problems, and other disease states. An abnormal duration (0.1 seconds) can indicate a blockage in the ventricle. An abnormal amplitude can indicate coronary disease, emphysema and obesity.
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Inside the QRS wave is a smaller wave. This wave is the relaxation of the atrium; it resembles an inverse P wave. It is far smaller in magnitude than the QRS and is therefore obscured by it.
ST segment This ST segment is a period of zero voltage that follows the QRS complex. This is the time period in between contraction of the ventricles. For certain diseases the ST segment can become depressed or elevated.
T wave The T wave represents the relaxation of the ventricles. The T wave is examined for its (A) direction, (B) shape and (C) height. A normal T wave is slightly round and asymmetrical. A pointed wave is cause of concern. A Tall T wave is a definite indicator of certain heart disease.
U wave Sometimes a small positive U wave may be seen to follow the T wave; this is due to the final relaxation of the ventricles. An inverted U wave of a prominent can underlying pathology.
Q-T interval The Q-T interval represents the total time taken for ventricles to contract and relax. This interval can range from 0.2 to 0.4 of a second.
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3.0 System Overview This chapter gives a system overview of the project. Example can get sample of ECG signals and what process can be applied to them.
3.1 From signals to samples
In the previous chapter we saw that the heart produces an ECG signal which can be monitored. For research purpose, ECG signals have been collected and stored in a database, called the MIT-BIH database. The signal are examined with the PanTompkins algorithm and then sent for Fourier analysis. Finally the results are sent to
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the Artificial Neural Network. This can be representing by a flow-chart as follow:
ECG Signal
MIT-BIT Database
Pan Tomkins Ailgorithm
Individual Beats
Find Times of P, Q, R,
Fast Fourier Transform
Time for QRS Complex
Frequency Response Of Beats
3.2 MIT-BIT Database In the 1970s Beth Israel Hospital (BIH) and Massachusetts Institute of Technology (MIT) collaborated in research into arrhythmia. [3] They examined the hospital records to produce a database of ECG waveforms. From hospital records twenty three recording were picked at random from a set of 4000. Twenty five records with abnormal ECG were also collect for the same data. This is done on purpose for
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research, as out of forty eight records you would not usually get twenty five abnormal records. Each record was independently noted with an explanation, to include background information on the subjects, including their medications. Each record is thirty minutes long and was digitized at 360 samples per second: this gives 648,000 samples in a 30 minute record. To analyse these records a MATLAB program was used [4]. MATLAB stand for matrix laboratory. It is a computer programming language developed in the 1970 by Cleve Moler to replace Fortran. Today it is used by engineers all over the world. In each record there are three files that make up the data; the hea file, atr file and a dat file. To interpret this file we use a MATLAB program created by Robert Tratnig (Vorarlberg University) was used. The MIT-BIH database was encoded in the 212 format. Robert Tratnig‟s code converted the database to binary data. This data was used throughout the project. In the programme, the number of samples to be read can be adjusted up to a maximum 648,000 samples. This point proved to be important when graphing the data.
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ECG signal 100.dat 1 0.8 0.6 0.4 V m 0.2 / e g a 1 0 t l 28 o V
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Fig 3.1: ECG from MIT-BIH database
Fig. 3.1 show a ten second time frame of the ECG signal. The frequency response is the discrete Fourier Transform of t he impulse.
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4.0 QRS Detection Chapter 4 explains the importance of the QRS complex and the Pan-Tompkins algorithm to detect it. Using the Algorithm, the R peak in the QRS complex can be found; this leads to getting the exact duration of the QRS complex.
4.1 Introduction The QRS complex is the most important complex in the ECG. The duration and amplitude should be measured as accurately as possible. There are two methods for highlight the QRS complex [5]: 1. Derivative-based methods. 2. Pan-Tompkins algorithm. Derivative-based methods depend on the fact that the QRS complex has the greatest slope and the sharpest turning point. It is also the highest point in the cardiac cycle. Rate of change is another name for the sharpest turning point, and we can find this using the derivative operator (d/dt). In principle the derivative operator will suppresses the P and T waves and highlight the QRS complex. However inside the QRS wave is a smaller wave; this is due to the relaxation of the atrium. While the wave can not be seen it gives rise to a peak above the QRS complex for a very short time interval. A QRS detection method based only on the derivative operator will give misleading results. In 1985 Pan and Tompkins proposed a new method for detection: the QRS complex. This method is an advance on the derivative-based method and also tries to eliminate noise for the ECG signal. This is now called the Pan-Tompkins algorithm.
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4.2 Pan-Tompkins algorithm
Pan-Tompkins algorithm proposes a real-time QRS detection algorithm based on slope, amplitude and width of the QRS complexes.[6] In this algorithm the ECG signal pass though a series of stages, is shown in the following block diagram fig.4.1.
Figure 4.1: Pan-Tompkins algorithm
The purpose of the band-pass filter is to pass in frequencies inside certain range and reject frequencies outside this range. In this project the range is between 5Hz and 60Hz. The purpose of the band-pass filter is to emphasize the QRS-complex and attenuate other parts of the ECG wave and the noise; thus the band-pass filter should cover the frequency band of the QRS complex. When the MATLAB function freqz.m is applied to the band-pass filter, the graphs below are obtained. The graphs in fig.4.2 show the frequency response in magnitude and phase. The Frequency Response typically measures magnitude response in dB and phase in radians.
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Figure 4.2: Plot of frequency response
When the signal has gone through the Band-pass filter, apply the MATLAB function diff.m to differentiate the signal. This suppresses the P and T waves. The next stage is to square the signal; this makes all the results positive and emphasises the QRS complex, as shown in fig.4.3.
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Fig. 4.3: Signal squared in Pan-Tompkins algorithm
The signal now passes through a Moving-Window integrator. A MovingWindow integrator is used because there are multiple peaks within the duration of a single QRS; the integrator takes an average of N samples, where N is the window width, and this is done by using a FIR filter. Havin g passed though this stage the QRS complex is sharply defined.
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4.3 Finding the QRS peaks
The output so far is a series of mV readings of the ECG. These are stored in a vector of length equal to the number of sample. There are 360 samples per second; the task now is to find the peak reading in the sample. Using MATLAB each sample was investigated individually. If the value of the sample is greater than the given threshold there is a peak, this is the R in the QRS complex and these are stored in an array, which notes the sample number as they occurred in the record. This gives the time (and sample number) of the R in the QRS complex. To change the sample number to seconds divide by 360. The fig.4.4 shows the difference in magnitude from one beat to the next.
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Fig. 4.4: Difference in magnitude for successive beats
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4.4 Getting individual beats
Using MATLAB a programme was devised which went through all the samples again. Using subtraction, the programme found the sample number half way between each beat. For example: Suppose there are beats at: Sample[60,70,84]. S1 = Sample (j) + 0.5(Sample (j+1) – Sample (j)) S1 = 60 + 0.5(70-60) = 65 S2 = Sample (j+1) + 0.5(Sample (j+2) – Sample (j+1)) S2 = 70 + 0.5(84-70) = 77 The output from this part of the programme is shown in fig.4.5:
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The points P, Q, R, S and T are clearly visible on this graph.
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4.5 Exact times of the QRS complex
From the data obtained so far, it is possible to find the exact time of the R complex. This is important for pattern recognition of a heart beat. The time of the R complex was found by using the max function of MATLAB on one complete cardiac cycle. In the example mentioned previously there is a peak at sample 70; so a complete cycle goes from samples 65 to 77. If there is a peak at sample 70, the min function in MATLAB will find the lowest point between samples 65 and 70, i.e. the Q complex. If the function is applied to samples 70 to 77, then the S complex will be found. A similar process could be applied to find the max at P and T; this could be more difficult as the P and T peaks are not as pronounced. Finally, if the time for Q and S are known the times of the QRS complex can be found. The duration of the QRS complex is usually 0.06 seconds (60ms) to 0.1 seconds (10ms). If the duration of the QRS complex is prolonged more than 0.1 sec, it is an indicator of certain heart diseases.
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5.0 Fourier Analysis Chapter 5 outline the 19 th century Fourier Transform and the 20 th century Fast Fourier Transform. The Fast Fourier Transform is implemented by using a direct command in MATLAB.
5.1 Fourier Transform
Fourier analysis is a family of mathematical techniques; all based on decomposing signals into sin and cosine functions. Fourier analysis and its transform are called after Joseph Fourier, a French mathematician and physicist in the 1800s. [ 7] In 1822 he published his famous work, Theorie analytique de La chaleur (the analytical theory of heat). This was the first work to use t he Fourier series. He is also credited with the discovery of the greenhouse effect in 1824. Fourier laid the foundation for the Fast Fourier Transform which is used by scientists and engineers today. For digital systems the Discrete Fourier Transform is be used. The formula for Discrete Fourier transform is:
It transforms the signal from time domain to the frequency domain representation. The formula for Inverse Discrete Fourier transform is:
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It transforms the signal from frequency domain back to the time domain representation. Both these formulas require very lengthy calculation.
5.2 Fast Fourier Transform
In 1965 J.W. Cooley and J. Tukey came up with a method for speeding up calculations of the Discrete Fourier transform [8]. It is now called the Cooley-Tukey algorithm for the Fast Fourier Transform. Later, it was found that the algorithm was already known to Carl Friedrick Gauss around 1805. Unfortunately, his paper was published in Latin after his death and it did not have a wide audience. The Fast Fourier Transform is an algorithm to compute the discrete Fourier transform and its inverse, reducing computation time by a factor of hundreds. [9] The difference in speed can be substantial especially for large amount of data. Fast Fourier Transform is used in a wide range of applications, from digital signal processing and partial differential equations to algorithms for multiplication of large integers. A Discrete Fourier Transform decomposes a sequence of values into components of different frequencies, calculating a Discrete Fourier Transform from the definition requires O(n2) operations an Fast Fourier Transform can find the same result in O(N log2(N)) operations.
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Fig.5.1: FFT method vs original method
As should in fig.5.1, 4096 point DFT will be calculated in last than a second with the Fast Fourier Transform, but will take nearly 1000 seconds with the original method [10].
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5.3 Implementation of the Fourier Transform In MATLAB program, the ECG signal passes through the Pan-Tompkins algorithm. The program then separates out individual beats as shown in fig.5.1.
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Fig. 5.2: One complete cardiac cycle with large DC component
This graph has a large D.C. component; another filter can be applied to the signal. A filter with the following transfer function was used.
H(z) = (1-z-1)/(1-az-1) where a = 0.97 After the second filter the result output is shown in fig.5.3.
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Fig. 5.3: One complete cardiac cycle without DC component
There is a direct command in MATLAB to implement the Fast Fourier Transform. The command is fft.
Y= fft (X)
Y is the Fast Fourier Transform of the vector X. Each vector X must have the same number of points n in the transform. You can add a second argument to fft to achieve this. Y= fft (X, N) . Now fft pads X with trailing zeros if the number of elements in X is less than N[11]. In this program N = 512, i.e. 512 samples were sent to the Fast Fourier Transform. An ECG signal is even periodic; this means only half the results need to be retained. This will reduce the memory requirements which are important with very large amounts of data. To calculate the Power Spectral Density (PSD), you must find the absolute value of the vector Y, now using 256 points as example above. This is done by
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multiplying Y by its complex conjugate. An example of the PSD for an ECG signal is shown in fig.5.4.
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Fig.4.5: FFT of complete cardiac cycle filtered
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6.0 Artificial Neural Network This Chapter explain how a Artificial Neural Network operates the long training programme for ECG data is outlined. The importance of getting reliable results is emphasised.
6.1 ANN as applied to ECG signals When the ECG waves have been processed, they must be classified into 2 classes: normal or abnormal. As the ECG wave is very complex 2 classes will not be sufficient. In this project the classifier that will be used is the Artificial Neural Network (ANN). AAN is a computer based system based on the Neural Networks in human biology. Neural Networks are useful for pattern recognition and non-linear systems. The function of network depends on the connection between the different elements (neurons). These connections are called weights. The basic processes are shown in fig.6.1.
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Fig. 6.1: Artificial Neural Network
The output is compared with the desired target. The weights in the neural network are changed to help achieve the target; these changes are called training a network. ANN will need a lot of training to correctly classify the various features of an ECG wave. One difficulty with ANN is the need for a very high degree of accuracy and reliability. The issue of false positives (normal ECG but gives abnormal result) and false negatives (abnormal ECG, but test give a normal result) needs to be addressed. The latter could be a life threatening error, while the former is a nuisance to doctors, as it generates more work. ANN suffers from high sensitivity to noise and often have difficulty dealing with ambiguous ECG patterns. Hence there is a need for very long training programme on existing record data, before it can be used on live patients. There are various types of ANN, these include Bayesian method, Fourier Transform Neural Networks, recurrent Neural Networks and back propagation Neural Networks. The input data from an ECG signal could comprise the following: QRS duration, P-R internal, Q-R internal, T interval and P interval. This information program has two targets for ANN:
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1. Direct classification normal / abnormal 2. Probability result from Direct classification associated with it.
The input data from the ECG should be divided into 2 sections: training data and testing data. Each result from the testing data will have a probability associated with it. A probability of 0.8 or 0.9 is fairly certain, but what about 0.5? This result has only a 50% probability of being right, i.e. it is very uncertain. It might be better to have 3 classifications (Normal, Abnormal and Uncertain). At least in the initial stages of training and testing. This system would reduce workload of doctors, and would now have to review only the uncertain cases. [12] As people live longer, there are an increasing number of people with heart trouble who need constant monitoring. An automated computer system using ANN would reduce the work load of doctor in busy hospitals.
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7.0 Results and Conclusion This chapter presents the results which were obtained during the project. Suggestions for further work are also given. The following results were obtained during the pr oject. A sample ECG signal was obtained from the MIT-BIH database. A 1.8 second time frame from the database is shown in fig.7.1. ECG signal 100.dat 1 0.8 0.6
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Figure 7.1: 1.8 second time frame of ECG from MIT-BIT database
The ECG signal passes through a band-pass filter and the frequency response in shown fig. 7.2.
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Fig. 7.2 Plot of frequency Response
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Fig.7.3 show the output when the signal is squared. This makes all the results positive and emphasises the QRS complex. The magnitude is easily seen in the graph.
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Fig. 7.4: One complete cardiac cycle
The timing of each individual beat was obtained and a sample cardiac cycle is shown in fig.7.4
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Fig. 7.5: FFT of cardiac cycle
Fig.7.5 show the output from the Fast Fourier Transform for the data using 512 points. An ECG signal is even periodic; this means that only half the results need to be retained.
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Figure 7.6: Half the FFT of cardiac cycle
Fig. 7.6 show half FFT which is all that needs to be taken into account for analysis. Areas of the project that could be developed further are: 1. More work on the timing information from the ECG Signal. 2. Statistical analysis on the timing parameters (interval statistics). 3. The data could be sent to an Artificial Neural Network for t raining purposes. 4. The MATLAB program could be converted to a C program. 5. As well as the Fourier Transform other front end processors could be used, e.g. the Wavelet Transform. 6. As well as the Artificial Neural Network other classifiers could be used, e.g. Linear Discriminant Analysis.
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7. A database of standard results could be developed for reference purposes. The project has been very interesting and informative and has great potential in the medical field. However, much work remains to be done.
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8.0 References [1] http://www.ecglibrary.com/ecghist.html 28th November 2008 [2] http://www.cvphysiology.com/Arrhythmias/A009.htm 04/06/07 [3] http://www.physionet.org/physiobank/database/mitdb/ 16-Mar-2009 [4] www.matworks.com [5] http://www.baskent.edu.tr/~byilmaz/teaching/BME402/BSPII-ch4-eventdetection1.pdf [6] http://courses.essex.ac.uk/ce/ce804/Pan-Tompkins%20algorithm.pdf [7] http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Fourier.html January 1997 [8] Mathematics Computation, Volume 19, 1965, pp297-301. [9], [10] S.W. Smith, “The Scientist and Engineer‟s Guide to DSP”, (California Technical Publishing, 1997) p.225. [11] http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdes k/help/techdoc/ref/fft.html [12] Arrhythmia Identification from ECG signals with Neural Network Classifier Based on Bayesian Framework, Dept. of Information Technology NUI Galway, Ireland
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9.0 Bibliography Application of artificial Neural Networks for ECG Signal Detection and Classification Journal of Electrocardiology Volume 26 supplement S.W. Smith” The Scientist and Engineer‟s Guide to DSP”, (California Technical Publishing 1997) http://web.mit.edu/6.555/www/ http://ecg.mit.edu 22 July 2005 Grey‟s Anatomy of the human body by Henry Grey L.B. Jackson “Signal, System and Transforms”, ( Addison-Wesley Publishing Company, Inc.) 1991
