Abstract
Introduction
Premature Ventricular Contraction (PVC) is among the most common types of ventricular cardiac arrhythmia. However, it only poses danger if the person suffers from a heart disease, such as heart failure. Hence, this is an important factor to consider in heart disease people. This paper presents an ECG realtime analysis system for PVC detection.
Methods
This system is based on threshold adaptive methods and Redundant Discrete Wavelet Transform (RDWT), with a realtime approach. This analysis is based on wavelet coefficients energy for PVC detection. It is presented also a study to find the most indicated wavelet mother for ECG analysis application among the following wavelet families: Daubechies, Coiflets and Symlets. The system detection performance was validated on the MITBIH Arrhythmia Database.
Results
The best results were verified with db2 wavelet mother: the Sensitivity Se = 99.18%, Positive Predictive Value P+ = 99.15% and Specificity Sp = 99.94%, on 80.872 annotated beats, and 61.2 s processing speed for a halfhour record.
Conclusion
The proposed system exhibits reliable PVC detection, with realtime approach, and a simple algorithmic structure that can be implemented in many platforms.
Keywords
Electrocardiogram; Premature ventricular contraction; Redundant Discrete Wavelet Transform
Introduction
Cardiovascular diseases are among the leading causes of death in the world. According to the World Health Organization (WHO), about 30% of these causes of death worldwide are related to cardiovascular problems. These numbers are closely linked to people’s lifestyle and been increasing every year, generating greater concern on many health organizations (World..., 2017 World Health Organization. WHO methods and data sources for country‐level causes of death 2000‐2015 [Internet]. Geneva: WHO; 2017 [cited 2018 Feb 28]. Available from: http://www.who.int/healthinfo/global_burden_disease/GlobalCOD_method_2000_2015.pdf?ua=1
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). More effective health actions are required, like prevention programs, diagnosis and treatment. In this sense, several technologies and methods have been developed to improve the health service in order to reduce the number of deaths and the costs involved with the healthcare system interventions ( Braunwald et al., 2002 Braunwald E, Antman EM, Beasley JW, Califf RM, Cheitlin MD, Hochman JS, Jones RH, Kereiakes D, Kupersmith J, Levin TN, Pepine CJ, Schaeffer JW, Smith EE 3rd, Steward DE, Theroux P, Gibbons RJ, Antman EM, Alpert JS, Faxon DP, Fuster V, Gregoratos G, Hiratzka LF, Jacobs AK, Smith SC Jr. ACC/AHA 2002 guideline update for the management of patients with unstable angina and non–stsegment elevation myocardial infarction: summary article. A report of the American College of Cardiology. J Am Coll Cardiol. 2002; 40(7):136674. http://dx.doi.org/10.1016/S07351097(02)023367. PMid:12383588.
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; Valentim et al., 2015 Valentim RAM, Araújo BG, Guedes TAL. A telessaúde no Brasil e a inovação tecnológica na atenção primária. Natal: EDUFRN; 2015. ).
Currently, an alternative that have been improved in the primary healthcare system is the telecardiology, which enables patients telemonitoring, ensuring continuous vital signs monitoring, and provide greater mobility and comfort for patients ( Chong et al., 2015 Chong JW, Esa N, McManus DD, Chon KH. Arrhythmia discrimination using a smart phone. IEEE J Biol Health Info. 2015; 19(3):81524. PMid:25838530. ; Gagnon et al., 2006 Gagnon MP, Duplantie J, Fortin JP, Landry R. Implementing telehealth to support medical practice in rural/remote regions: what are the conditions for success? Imp Sci. 2006; 1(1):18. http://dx.doi.org/10.1186/17485908118. PMid:16930484.
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; Hersh et al., 2001 Hersh WR, Helfand M, Wallace J, Kraemer D, Patterson P, Shapiro S, Greenlick M. Clinical outcomes resulting from telemedicine interventions: A systematic review. BMC Med Inform Decis Mak. 2001; 1(1):18. http://dx.doi.org/10.1186/1472694715. PMid:11737882.
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; Valentim et al., 2015 Valentim RAM, Araújo BG, Guedes TAL. A telessaúde no Brasil e a inovação tecnológica na atenção primária. Natal: EDUFRN; 2015. ). In this way, the automatic detection of cardiac signals (electrocardiogram  ECG) is important to cardiac disease diagnosis, and can be used like medical diagnosis assistance tool. However, the automatic ECG analyzing systems performance depends heavily upon the reliable and accurate detection of the ECG signal characteristic (QRS complex, as well as the P and T waves) ( Dalvi et al., 2016 Dalvi RF, Zago GT, Andreao RV. Heartbeat classification system based on neural networks and dimensionality reduction. Res Biomed Eng. 2016; 32(4):31826. http://dx.doi.org/10.1590/24464740.05815.
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; Valentim et al., 2015 Valentim RAM, Araújo BG, Guedes TAL. A telessaúde no Brasil e a inovação tecnológica na atenção primária. Natal: EDUFRN; 2015. ).
In this work, an algorithm based on ECG signal with realtime approach has been developed in order to detect heart disease, in particular the Premature Ventricular Contraction (PVC) occurrence. The ECG reflects the heart electrical activity, it is a recording of the electric potential generated by electric behavior of the cardiac muscle tissue, the heart, and provides information about the heart state, enabling several noninvasive diagnostic of heart disease ( Clifford et al., 2006 Clifford GD, Azuaje F, McSharry PE, editors. Advanced methods and tools for ECG analysis. Vol. 1. Norwood: Artech House; 2006. (Series Engineering in Medicine and Biology). ; Malmivuo and Plonsey, 1995 Malmivuo J, Plonsey R. Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford: Oxford University Press; 1995. http://dx.doi.org/10.1093/acprof:oso/9780195058239.001.0001.
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). Thus, a system that analyzes PVC is proposed, that is among the most common types of ventricular cardiac arrhythmia ( Mann et al., 2014 Mann DL, Zipes DP, Libby P, Bonow RO, editors. Braunwald’s heart disease: a textbook of cardiovascular medicine. Philadelphia: Saunders Elsevier; 2014. ; Morris et al., 2009 Morris F, Brady WJ, Camm J. ABC of clinical electrocardiography. USA: John Wiley & Sons; 2009. ; Natale, 2007 Natale A. Handbook of cardiac electrophysiology. Boca Raton: CRC Press; 2007. http://dx.doi.org/10.3109/9780203089866.
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).
The PVC is a cardiac rhythm abnormalities resulted from ectopic foci in the ventricles, and it is independent of the sinoatrial node pace set. It is frequently originated from the right ventricular outflow tract, but some can be originated from the left ventricular outflow tract, from aortic sinus cusp, from tricuspid and mitral valve annulus, and from coronary venous system, among other heart structures ( Ge et al., 2012 Ge B, Ji KT, Ye HG, Li J, Li YC, Yin RP, Lin JF. Electrocardiogram features of premature ventricular contractions/ventricular tachycardia originating from the left ventricular outflow tract and the treatment outcome of radiofrequency catheter ablation. BMC Cardiovasc Disord. 2012; 12(1):111. http://dx.doi.org/10.1186/1471226112112. PMid:23186541.
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; Jia et al., 2011 Jia L, YueChun L, KangTing J, NaDan Z, JiaXuan L, WenWu Z, PengLin Y, JiFei T, JiaFeng L. Premature ventricular contractions originating from the left ventricular septum: results of radiofrequency catheter ablation in twenty patients. BMC Cardio Disease. 2011; 11(1):18. http://dx.doi.org/10.1186/147122611127. PMid:21635765.
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; Sayadi et al., 2010 Sayadi O, Shamsollahi MB, Clifford GD. Robust detection of premature ventricular contractions using a wavebased Bayesian framework. IEEE Trans Biomed Eng. 2010; 57(2):35362. http://dx.doi.org/10.1109/TBME.2009.2031243. PMid:19758851.
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).
The PVC generates one heartbeat that occurs abnormally early of the normal sinus rhythm, and usually it is not associated with P wave. This electrical event usually causes a break in the normal sinus heart activity — this break results from the gap between the PVC and the next normal heartbeat and is called compensatory pause ( Malmivuo and Plonsey, 1995 Malmivuo J, Plonsey R. Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford: Oxford University Press; 1995. http://dx.doi.org/10.1093/acprof:oso/9780195058239.001.0001.
http://dx.doi.org/10.1093/acprof:oso/97...
; Mann et al., 2014 Mann DL, Zipes DP, Libby P, Bonow RO, editors. Braunwald’s heart disease: a textbook of cardiovascular medicine. Philadelphia: Saunders Elsevier; 2014. ; Natale, 2007 Natale A. Handbook of cardiac electrophysiology. Boca Raton: CRC Press; 2007. http://dx.doi.org/10.3109/9780203089866.
http://dx.doi.org/10.3109/9780203089866...
).
The PVC can occurs in person of any age and not necessarily represent cardiac risk, however it only pose danger if the person has any heart disease, such as heart failure. Thus, this is an important factor to consider in heart disease people. Recent studies indicate that the PVC can be an indicative of sudden cardiac death risk, and it is associated with mortality from acute myocardial infarction ( Hirose et al., 2010 Hirose H, Ishikawa S, Gotoh T, Kabutoya T, Kayaba K, Kajii E. Cardiac mortality of premature ventricular complexes in healthy people in Japan. J Cardiol. 2010; 56(1):236. http://dx.doi.org/10.1016/j.jjcc.2010.01.005. PMid:20350513.
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; Inan et al., 2006 Inan OT, Giovangrandi L, Kovacs GTA. Robust neuralnetworkbased classification of premature ventricular contractions using wavelet transform and timing interval features. IEEE Trans Biomed Eng. 2006; 53(12):250715. ; Iwasa et al., 2005 Iwasa A, Hwa M, Hassankhani A, Liu T, Narayan SM. Abnormal heart rate turbulence predicts the initiation of ventricular arrhythmias. Pac Clin Electroph. 2005; 28(11):118997. http://dx.doi.org/10.1111/j.15408159.2005.50186.x.
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). Therefore, the PVC detection has a particular interest for patients with heart disease treatment.
Hence, in the last years, several PVC detection system have been proposed for this issue: based on Artificial Neural Network (ANN) ( Bortolan et al., 1991 Bortolan G, Degani R, Willems JL. ECG classification with neural networks and cluster analysis. Proc in Comp in Cardio. 1991; 1991:17780. ; Dalvi et al., 2016 Dalvi RF, Zago GT, Andreao RV. Heartbeat classification system based on neural networks and dimensionality reduction. Res Biomed Eng. 2016; 32(4):31826. http://dx.doi.org/10.1590/24464740.05815.
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; Hu et al., 1997 Hu YH, Palreddy S, Tompkins WJ. A patientadaptable ecg beat classifier using a mixture of experts approach. IEEE Trans Biomed Eng. 1997; 44(9):891900. http://dx.doi.org/10.1109/10.623058. PMid:9282481.
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; Inan et al., 2006 Inan OT, Giovangrandi L, Kovacs GTA. Robust neuralnetworkbased classification of premature ventricular contractions using wavelet transform and timing interval features. IEEE Trans Biomed Eng. 2006; 53(12):250715. ), Heuristic algorithm ( Dotsinsky and Stoyanov, 2004 Dotsinsky IA, Stoyanov TV. Ventricular beat detection in single channel electrocardiograms. Biomed Eng Online. 2004; 3(1):19. http://dx.doi.org/10.1186/1475925X33. PMid:14750981.
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), Bayesian framework ( Sayadi et al., 2010 Sayadi O, Shamsollahi MB, Clifford GD. Robust detection of premature ventricular contractions using a wavebased Bayesian framework. IEEE Trans Biomed Eng. 2010; 57(2):35362. http://dx.doi.org/10.1109/TBME.2009.2031243. PMid:19758851.
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), Support Vector Machine (SVM) ( Shen et al., 2011 Shen Z, Hu C, Li P, Meng MQH. Research on premature ventricular contraction realtime detection based support vector machine. In: 2011 IEEE International Conference on Information and Automation (ICIA); 2011 June 68; Shenzhen, China. USA: IEEE; 2011. p. 8649. http://dx.doi.org/10.1109/ICINFA.2011.5949116.
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), morphology ECG features ( Chazal and Reilly, 2006 Chazal P, Reilly RB. A patientadapting heartbeat classifier using ecg morphology and heartbeat interval features. IEEE Trans Biomed Eng. 2006; 53(12 Pt 1):253543. http://dx.doi.org/10.1109/TBME.2006.883802. PMid:17153211.
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; Chazal et al., 2004 Chazal P, O’Dwyer M, Reilly RB. Automatic classification of heartbeats using ecg morphology and heartbeat interval features. IEEE Trans Biomed Eng. 2004; 51(7):1196206. http://dx.doi.org/10.1109/TBME.2004.827359. PMid:15248536.
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; Lekuthai et al., 2014 Lekuthai A, Ittatirut S, Teeramongkonrasmee A. Algorithm development for realtime detection of premature ventricular contraction. In: TENCON 2014  2014 IEEE Region 10 Conference; 2014 Oct 2225; Bangkok, Thailand. USA: IEEE; 2014. p. 15. http://dx.doi.org/10.1109/TENCON.2014.7022418.
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), Fuzzy Neural Network System (FNNS) ( Lim, 2009 Lim JS. Finding features for realtime premature ventricular contraction detection using a fuzzy neural network system. IEEE Trans Neural Netw. 2009; 20(3):5227. http://dx.doi.org/10.1109/TNN.2008.2012031. PMid:19179246.
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), Wavelet Transform ( Inan et al., 2006 Inan OT, Giovangrandi L, Kovacs GTA. Robust neuralnetworkbased classification of premature ventricular contractions using wavelet transform and timing interval features. IEEE Trans Biomed Eng. 2006; 53(12):250715. ; Martis et al., 2013 Martis RJ, Acharya UR, Min LC. ECG beat classification using PCA, LDA, ICA and discrete wavelet transform. Biomed Signal Process Control. 2013; 8(5):43748. http://dx.doi.org/10.1016/j.bspc.2013.01.005.
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; Nazarahari et al., 2015 Nazarahari M, Ghorbanpour Namin S, Davaie Markazi AH, Kabir Anaraki A. A multiwavelet optimization approach using similarity measures for electrocardiogram signal classification. Biomed Sig Proc Cont. 2015; 20(400):14251. http://dx.doi.org/10.1016/j.bspc.2015.04.010.
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; OrozcoDuque et al., 2013 OrozcoDuque A, MartinezTabares FJ, Gallego J, Rodriguez CA, Mora ID, CastellanosDominguez G, et al. Classification of premature ventricular contraction based on discrete wavelet transform for real time applications. In: Health Care Exchanges (PAHCE) 2013 Pan American; 2013 Apr 29May 4; Medellin, Colombia. USA: IEEE; 2013. p. 15. http://dx.doi.org/10.1109/PAHCE.2013.6568330.
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) and adaptive filter ( Nieminaki et al., 1999 Nieminaki M, Ruha A, Kemppainen J, Nissila S, Myilyla R. Realtime detection of premature ventricular contraction using a matched filter bank. In: Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society; 1999 Oct 1316; Atlanta, GA, USA. USA: IEEE; 1999. p. 269. http://dx.doi.org/10.1109/IEMBS.1999.802338.
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). The main feature of most detection methods is a realtime analysis, however some methods have high mathematical complexity, which demands a high computational cost.
This paper presents a Waveletbased algorithm for PVC detection, with a realtime approach. Adaptive threshold methods were used in parallel with the Wavelet Transform and the system was validated on MITBIH Arrhythmia Database ( Moody and Mark, 2001 Moody G, Mark R. The impact of the mitbih arrhythmia database. IEEE Eng Med Biol Mag. 2001; 20(3):4550. http://dx.doi.org/10.1109/51.932724. PMid:11446209.
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Methods
Wavelet transform
The Wavelet Transform (WT) has been widely used in recent years in various areas and several applications, such as power system quality ( Andrade and Leao, 2014 Andrade L, Leao MTP. Fault location for transmission lines using wavelet. IEEE Latin Am Trans. 2014; 12(6):10438. http://dx.doi.org/10.1109/TLA.2014.6893998.
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; Costa, 2014 Costa FB. Boundary wavelet coefficients for realtime detection of transients induced by faults and powerquality disturbances. IEEE Trans Power Deliv. 2014; 29(6):267487. http://dx.doi.org/10.1109/TPWRD.2014.2321178.
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), signal processing ( Pedireddi and Srinivasan, 2010 Pedireddi LB, Srinivasan B. Characterization of atmospheric turbulence effects and their mitigation using waveletbased signal processing. IEEE Trans Commun. 2010; 58(6):1795802. http://dx.doi.org/10.1109/TCOMM.2010.06.090194.
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; Saleh et al., 2012 Saleh SA, Ahshan R, Moloney CR. Waveletbased signal processing method for detecting ice accretion on wind turbines. IEEE Trans Sust Ener. 2012; 3(3):58597. http://dx.doi.org/10.1109/TSTE.2012.2194725.
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), biomedical engineering ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
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; Dalvi et al., 2016 Dalvi RF, Zago GT, Andreao RV. Heartbeat classification system based on neural networks and dimensionality reduction. Res Biomed Eng. 2016; 32(4):31826. http://dx.doi.org/10.1590/24464740.05815.
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; Di Marco and Chiari, 2011 Di Marco LY, Chiari L. A waveletbased ECG delineation algorithm for 32bit integer online processing. Biomed Eng Online. 2011; 10(1):119. http://dx.doi.org/10.1186/1475925X1023. PMid:21457580.
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; Kim et al., 2011 Kim J, Min SD, Lee M. An arrhythmia classification algorithm using a dedicated wavelet adapted to different subjects. Biomed Eng Online. 2011; 10(1):119. http://dx.doi.org/10.1186/1475925X1056. PMid:21707989.
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; Madeiro et al., 2009 Madeiro JPV, Cortez PC, Marques JAL. Performance comparison analysis of Wavelet and Hilbert transforms for QRS detection in ECG. Rev Bras Eng Bioméd. 2009; 25:15366. http://dx.doi.org/10.4322/rbeb.2012.072.
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), among others. WT provides a compact and flexible analysis in time and frequency domain, allowing different resolution levels, besides presenting various base functions (Wavelet families), which allow a more specific analysis in order to adapt the analysis of signal behavior and so achieve the best possible results ( Burrus et al., 1997 Burrus CS, Gopinath RA, Guo H. Introduction to wavelets and wavelet transforms: a primer. New Jersey: Prentice Hall; 1997. ; Mallat, 1989 Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell. 1989; 11(7):67493. http://dx.doi.org/10.1109/34.192463.
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, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
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).
WT allows multiresolution analysis, such that a discrete signal can be decomposed and analyzed at different resolution levels (or scales) ( Burrus et al., 1997 Burrus CS, Gopinath RA, Guo H. Introduction to wavelets and wavelet transforms: a primer. New Jersey: Prentice Hall; 1997. ; Mallat, 1989 Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell. 1989; 11(7):67493. http://dx.doi.org/10.1109/34.192463.
http://dx.doi.org/10.1109/34.192463 ...
, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ). Thus, a discretized signal can be decomposed in terms of wavelet coefficients and scaling coefficients at various levels of resolution through a digital filtering process. This filtering process divides the input signal into two frequency bands, high frequency signals and low frequency signals. The wavelet coefficients is the highpass filters results and the scaling coefficients is the lowpass filters results ( Burrus et al., 1997 Burrus CS, Gopinath RA, Guo H. Introduction to wavelets and wavelet transforms: a primer. New Jersey: Prentice Hall; 1997. ; Mallat, 1989 Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell. 1989; 11(7):67493. http://dx.doi.org/10.1109/34.192463.
http://dx.doi.org/10.1109/34.192463 ...
, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
http://dx.doi.org/10.1017/CBO9780511841...
).
Wavelet Transforms can be used for continuous time (Continuous Wavelet Transform  CWT) or discrete time (Discrete Wavelet Transform  DWT) signals applications. In relation to basic functions there are several Wavelet families as Morlet, Biorthogonal, Mexican Hat, Harr, Daubechies, Meyer, Coiflets, Symlets, and many others, both in the Real domain and Complex domain numbers ( Daubechies, 1992 Daubechies I. Ten lectures on wavelets. Canada: Siam; 1992. (CBMSNSF Regional Conference Series in Applied Mathematics). http://dx.doi.org/10.1137/1.9781611970104.
CBMSNSF Regional Conference Series in ...
; Grossmann and Morlet, 1984 Grossmann A, Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal. 1984; 15(4):72336. http://dx.doi.org/10.1137/0515056.
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; Mallat, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
http://dx.doi.org/10.1017/CBO9780511841...
).
For cardiac signal analysis the Wavelet family most used is the Daubechies, especially the mother Wavelet db4 ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
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; Sasikala and Wahidabanu, 2010 Sasikala P, Wahidabanu R. Robust r peak and qrs detection in electrocardiogram using wavelet transform. Inter J of Advan Comp Sci and AppIJACSA. 2010; 1(6):4853. ; Singh and Tiwari, 2006 Singh BN, Tiwari AK. Optimal selection of wavelet basis function applied to ECG signal denoising. Dig Sig Proc. 2006; 16(3):27587. http://dx.doi.org/10.1016/j.dsp.2005.12.003.
http://dx.doi.org/10.1016/j.dsp.2005.12...
). However, the ECG signal analysis with db4 explanation is not clear in this works. In this paper is used the Redundant Discrete Wavelet Transform (RDWT), a DWT variant version, and is compared the system performance with some mother wavelets from Daubechies, Coiflets and Symlets Wavelet families in order to find the best mother wavelet for ECG signals analysis application.
Redundant discrete wavelet transform
RDWT is a DWT variant version, and presents the basic characteristics of it: the original signal is decomposed into two components, wavelet and scaling coefficients, and the filter coefficients for the calculation of each component are related, the highpass and lowpass filters, respectively ( Daubechies, 1992 Daubechies I. Ten lectures on wavelets. Canada: Siam; 1992. (CBMSNSF Regional Conference Series in Applied Mathematics). http://dx.doi.org/10.1137/1.9781611970104.
CBMSNSF Regional Conference Series in ...
; Grossmann and Morlet, 1984 Grossmann A, Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal. 1984; 15(4):72336. http://dx.doi.org/10.1137/0515056.
http://dx.doi.org/10.1137/0515056 ...
; Mallat, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
http://dx.doi.org/10.1017/CBO9780511841...
). Although the DWT provides relatively simple implementation complexity, speed and low computational effort, the RDWT has become interesting due to the fact that DWT present some limitations for some specific applications such as the detection of the QRS complex in realtime analysis ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
http://dx.doi.org/10.1109/TLA.2016.7483...
).
The major difference between the DWT and RDWT is the subsampling process: the DWT presents time variant behavior due to the subsampling process used to calculate the wavelet and scaling coefficients, whereas the RDWT not present the subsampling process, so this mathematical tool provides time invariant behavior, resulting in less significant delay over the signal reconstruction process if compared to DWT ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
http://dx.doi.org/10.1109/TLA.2016.7483...
; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
http://dx.doi.org/10.1017/CBO9780511841...
). In general, the main differences are listed below:

RDWT can be applied to any number of samples, whereas DWT requires is a power of two number sample due to the subsampling process by two;

DWT is an orthonormal transformation, whereas RDWT is a non orthogonal transformation;

RDWT is an invariant time transform, since it does not perform subsampling process by two in the signal sample, whereas DWT performs the subsampling process by two, resulting in a time variant behavior.
The RDWT mathematical model for realtime approach is given by the following equations ( Arrais et al., 2014 Arrais E, Roda VO, Sousa CM No, Ribeiro RLA, Costa FB. FPGA versus DSP for wavelet transform based voltage sags detection. In: Proceedings 2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC); 2014 May 1215; Montevideo, Uruguay. USA: IEEE; 2014. p. 6437. http://dx.doi.org/10.1109/I2MTC.2014.6860822.
http://dx.doi.org/10.1109/I2MTC.2014.68...
; Costa and Driesen, 2013 Costa FB, Driesen J. Assessment of voltage sag indices based on scaling and wavelet coefficient energy analysis. IEEE Trans Power Deliv. 2013; 28(1):33646. http://dx.doi.org/10.1109/TPWRD.2012.2218626.
http://dx.doi.org/10.1109/TPWRD.2012.22...
): The Equation 1 provides the scaling coefficients, s_{j}, and the Equation 2 provides the wavelet coefficients, ω_{j}, both in the level resolution (scale) j, obtained by convolution of the scaling coefficients s_{j1} by $\tilde{g}$ and $\tilde{h}$ filters, of the scale j1. The $\tilde{g}$ is the lowpass filter coefficients and $\tilde{h}$ is the highpass filter coefficients for calculating the scaling and wavelet coefficients, respectively.
since $k\ge L1$: k is the current sampling in the realtime analysis and L is the length of the filters. The variable l is incremental variable of summation.
Figure 1 shows a decomposition process block diagram for RDWT of a signal x_{0} (s_{0}) with sampling frequency (f_{s} ) in two resolution level (first and second scale), that provides the scaling (s _{1} and s_{2}) and wavelet (ω _{1} and ω_{2}) coefficients. This decomposition process is based on the pyramidal algorithm of Mallat ( Mallat, 1989 Mallat SG. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell. 1989; 11(7):67493. http://dx.doi.org/10.1109/34.192463.
http://dx.doi.org/10.1109/34.192463 ...
, 2008 Mallat SG. A wavelet tour of signal processing: the sparse way. USA: Academic Press; 2008. ). The filters coefficients $\tilde{g}\text{}$ and $\tilde{h}$ are obtained based on the DWT filters (g and h) ( Costa and Driesen, 2013 Costa FB, Driesen J. Assessment of voltage sag indices based on scaling and wavelet coefficient energy analysis. IEEE Trans Power Deliv. 2013; 28(1):33646. http://dx.doi.org/10.1109/TPWRD.2012.2218626.
http://dx.doi.org/10.1109/TPWRD.2012.22...
; Percival and Walden, 2000 Percival AT, Walden DB. Wavelet methods for time series analysis. New York: Cambridge University Press; 2000. http://dx.doi.org/10.1017/CBO9780511841040.
http://dx.doi.org/10.1017/CBO9780511841...
), as defined below ( Equations 3 and 4 ):
Block diagram illustrating the RDWT decomposition process in two resolutions levels (or two resolutions scales). x_{0} is the original signal, s_{1} and s_{2} are the scaling coefficients on the first and second resolutions levels, respectively; ω _{1} and ω_{2} are the wavelet coefficients in the first and second resolutions levels, respectively; $\tilde{g}\text{}$ and $\tilde{h}$ are the lowpass and highpass filters coefficients, respectively.
The signal energy can be calculated based on the scaling and wavelet coefficients: in according to Parseval’s theorem, the signal energy can be partitioned in terms of the wavelet and scaling coefficients energy ( Burrus et al., 1997 Burrus CS, Gopinath RA, Guo H. Introduction to wavelets and wavelet transforms: a primer. New Jersey: Prentice Hall; 1997. ). In other words, the energy of the original signal x_{0}, with k_{t} sample, is equal to the sum of the wavelet coefficients energies of all resolution levels, 1 ≤ j ≤ J, with the scaling coefficients energy of the last resolution level, J, with J ≤ J_{max} ( Burrus et al., 1997 Burrus CS, Gopinath RA, Guo H. Introduction to wavelets and wavelet transforms: a primer. New Jersey: Prentice Hall; 1997. ; Costa and Driesen, 2013 Costa FB, Driesen J. Assessment of voltage sag indices based on scaling and wavelet coefficient energy analysis. IEEE Trans Power Deliv. 2013; 28(1):33646. http://dx.doi.org/10.1109/TPWRD.2012.2218626.
http://dx.doi.org/10.1109/TPWRD.2012.22...
). The energy signal can be calculated by Equation 5:
where:
Benchmark databases
Several standard ECG databases are available for the evaluation of heart disease detection algorithms ( Kohler et al., 2002 Kohler BU, Hennig C, Orglmeister R. The principles of software QRS detection. IEEE Eng Med Biol Mag. 2002; 21(1):4257. http://dx.doi.org/10.1109/51.993193. PMid:11935987.
http://dx.doi.org/10.1109/51.993193 ...
; Martis et al., 2014 Martis RJ, Acharya UR, Adeli H. Current methods in electrocardiogram characterization. Comput Biol Med. 2014; 48:13349. http://dx.doi.org/10.1016/j.compbiomed.2014.02.012. PMid:24681634.
http://dx.doi.org/10.1016/j.compbiomed....
). The algorithm performance on a standard database is not the main parameter to propose to apply in a clinical environment, but it provides a good performance comparison between algorithm detections. In this research work was used the MIT/BIH arrhythmia database, since it is one of the most used to evaluate the algorithm ECG detections ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
http://dx.doi.org/10.1109/TLA.2016.7483...
; Hamilton and Tompkins, 1986 Hamilton PS, Tompkins WT. Quantitative Investigation of QRS Detection Rules Using the MIT/BIH Arrhythmia Database. IEEE Trans Biomed Eng. 1986; 33(12):115765. http://dx.doi.org/10.1109/TBME.1986.325695. PMid:3817849.
http://dx.doi.org/10.1109/TBME.1986.325...
; Li et al., 1995 Li C, Zheng C, Tai C. Detection of ECG characteristic points using wavelet transforms. IEEE Trans Biomed Eng. 1995; 42(1):218. http://dx.doi.org/10.1109/10.362922. PMid:7851927.
http://dx.doi.org/10.1109/10.362922 ...
; Martinez et al., 2004 Martinez J, Almeida R, Olmos S, Rocha A, Laguna P. A waveletbased ecg delineator: evaluation on standard databases. IEEE Trans Biomed Eng. 2004; 51(4):57081. http://dx.doi.org/10.1109/TBME.2003.821031.
http://dx.doi.org/10.1109/TBME.2003.821...
; Pan and Tompkins, 1985 Pan J, Tompkins WJ. A realtime QRS detection algorithm. IEEE Trans Biomed Eng. 1985; 32(3):2306. http://dx.doi.org/10.1109/TBME.1985.325532. PMid:3997178.
http://dx.doi.org/10.1109/TBME.1985.325...
).
This database is obtained over 4,000 longterm Holter recordings at Beth Israel Hospital Arrhythmia Laboratory between the years of 1975 and 1979 from patients under different cardiac arrhythmias. It contains 48.5 hours of recordings with twochannel and sampling rate of 360 Hz. However, only one of the ECG channels was used (channel 1  a modified limb lead II (MLII)). However, the database contains records of modified leads V1, V2 and V5, and, in one instance, also V4. The subject’s records were obtained from 25 men aged 32 to 89 years, and 22 women aged 23 to 89 years ( Goldberger et al., 2000 Goldberger ALL, Amaral AN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, et al. Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals. Comp Cardio. 2000; 101(23):21520. PMID: 10851218. ; Moody and Mark, 2001 Moody G, Mark R. The impact of the mitbih arrhythmia database. IEEE Eng Med Biol Mag. 2001; 20(3):4550. http://dx.doi.org/10.1109/51.932724. PMid:11446209.
http://dx.doi.org/10.1109/51.932724 ...
). It was analyzed 36 recordings, although the database contains 48 recordings, by reason of external noise in some recordings that disturbed the ECG signal behavior.
System description
The system for PVC detection is based on the RDWT and adaptive threshold methods. It was described on Matlab 2014a platform version. The Figure 2 shows the system description flowchart. The RDWT provides two coefficients, the scaling and the wavelet coefficients, and the algorithm proposed is based on the energy wavelet coefficients for PVC detection. The ECG features is obtained with the RDWT and the detection process is through adaptive threshold methods based on mean value ECG signal energy on all resolution levels, therefore there is one threshold for each level.
System flowchart. The energy wavelet coefficients algorithm analysis is based on RDWT. The variable e[n] is the n sample energy wavelet coefficients. E_{p_aux} is an auxiliary variable used to store a temporary energy value sample. The thr is the threshold value used to detect the possible PVC occurrence. If the energy wavelet coefficient sample (e[n]) is higher than the threshold (thr), this sample is stored in the auxiliary variable E_{aux}. So, the algorithm compares each value E_{aux} with the next sample. Then, the current sample is stored in E_{aux} and the previous sample in the E_{p_aux}. When the current sample (E_{aux}) is less than the previous sample (E _{p_aux}), this sample is stored in a vector E_{P}[n] , and this indicates possible PVC. Thus, the ECG signal is analyzed and all indicative PVC occurrence is stored in a vector. This algorithm is computed for all scales, and each scale has one associated threshold value. Thus, the PVC occurrence can be detected in all scales, although the three last levels are predominant.
In the proposed system, each ECG signal sample (data record from MITBIH databases) is analyzed in realtime approach. The RDWTbased energy wavelet coefficients are analyzed to detect the PVC. Each energy wavelet coefficient sample is compared with a threshold value, and if it is higher than the threshold value, the sample is a possible PVC occurrence indicative. Hence, this sample is stored and will be compared with the next sample (remaining). Therefore, these selected samples are compared and the one that has the highest value (amplitude peak) corresponds to the energy maximum value and a PVC occurrence.
The energy PVC value is much higher than the normal ECG energy module value. For this reason that the PVC can be detect based on energy signal. The variable e[n] is the n sample energy wavelet coefficients, provided by RDWT. It is used an auxiliary variable E_{p_aux} to store a temporary energy sample value. The threshold value thr is obtained from empirical way, according to computed test, and it is used to detect the possible PVC occurrence. The threshold value is updated in according to the mean energy value in each minute ECG record.
If the energy wavelet coefficient sample (e[n]) is greater than the threshold (thr), this sample is stored in the auxiliary variable E _{aux}. Then, the algorithm compares each value E_{aux} with the next sample. Then, the current sample is stored in E_{aux} and the last sample in the E_{p_aux}. When the current sample (Eaux) is less than the previous sample (Epaux), this sample is stored in a vector E_{P}[n], and this indicates possible PVC. Thus, the ECG signal is analyzed and all indicative PVC occurrences are stored in a vector.
In this work the RDWT was implemented with six resolution levels (or scale). The sample frequency used was 350 Hz, in order to optimize the distribution of the ECG signal energy into resolution levels, to facilitate the signal analysis, according to ECG power spectra ( Thakor et al., 1984 Thakor N, Webster J, Tompkins WJ. Estimation of QRS complex power spectra for design of a qrs filter. IEEE Trans Biomed Eng. 1984; 31(11):7026. http://dx.doi.org/10.1109/TBME.1984.325393. PMid:6500590.
http://dx.doi.org/10.1109/TBME.1984.325...
). The Table 1 presents the frequency bands for each RDWT resolution level of the wavelet coefficients.
Results
In this paper it was analyzed the effect of the wavelet families Daubechies, Coiflets and Symlets, in order to find the best wavelet for ECG proposed analysis. This analyze motivation by virtue of many works use the mother wavelet db4 (Daubechies family), but the reason is not clear. The Table 2 shows the comparative results, based on standard deviation analysis between the ECG energy signal and the energy scaling coefficients at all resolution level. It was analyzed the following mother wavelets: Daubechies (db2, db4, db6, db8, and db12), Coiflets (coif6, coif12 and coif18) and Symlets (sym4, sym6, sym8 and sym10).
Comparative study among three Wavelet families for ECG signal analyses. Normalized standard deviation analysis between the ECG energy signal and the energy scaling coefficients at all resolution level. It was calculated for three Wavelet families and some of their mothers wavelets: Daubechies (db2, db4 db6, db8, and db12), Coiflets (coif6, coif12 and coif18) and Symlets (sym4, sym6, sym8 and sym10). It was computed the following recordings: 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 200, 201, 202, 203, 205, 207 and 208.
The energy coefficients standard deviation provides a good dispersion measure to verify the energy behavior ECG signal analyzed by the pyramidal algorithm, since the energy loss in the detection process will result in low performance. This analysis was computed for all resolution level in order to find the lowest variation of the standard deviation between the levels.
Based on the results the lowest mother wavelet filter order provides the best standard deviation between the energy original signal and the wavelet coefficients energy for each level. So, the reliability and effectiveness of cardiac signal analysis algorithms based on Wavelet Transform are closely linked to the wavelet filters order used, with better results for loworder filters. Thereby, due to this comparative study, it was chosen the Daubechies Wavelet family for signal analysis.
Although the study indicates that db2 is the best for ECG application, in this paper the mother Wavelets db2, db4, coif6 and sym4 were verified, in order to ascertain which provides the best performance, since these mother wavelets provided the lowest standard deviation value for their respective wavelet families. This motivation is also due to the large amount of works that use db4 for ECG analysis and the search for a faster algorithm.
The system was validated on MITBIH Arrhythmia Database ( Goldberger et al., 2000 Goldberger ALL, Amaral AN, Glass L, Hausdorff JM, Ivanov PC, Mark RG, et al. Physiobank, physiotoolkit, and physionet: Components of a new research resource for complex physiologic signals. Comp Cardio. 2000; 101(23):21520. PMID: 10851218. ; Moody and Mark, 2001 Moody G, Mark R. The impact of the mitbih arrhythmia database. IEEE Eng Med Biol Mag. 2001; 20(3):4550. http://dx.doi.org/10.1109/51.932724. PMid:11446209.
http://dx.doi.org/10.1109/51.932724 ...
), and the detection algorithms performance is evaluated according to three parameters, Sensitivity (Se), Positive Predictivity (P+) and Specificity (Sp) ( Kohler et al., 2002 Kohler BU, Hennig C, Orglmeister R. The principles of software QRS detection. IEEE Eng Med Biol Mag. 2002; 21(1):4257. http://dx.doi.org/10.1109/51.993193. PMid:11935987.
http://dx.doi.org/10.1109/51.993193 ...
; Wang, 2013 Wang J. Proposed new requirements for testing and reporting performance results of arrhythmia detection algorithms. In: Computing in Cardiology; 2013 Sept 2225; Zaragoza, Spain. USA: IEEE; 2013. p. 96770. ):
where TP is the True Positive, the FN is the False Negative, FP the False Positive and TN the True Negative values.
Figure 3 shows the algorithmic results based on db2 mother wavelet for the record 100 analysis from MITBIH Arrhythmia Database. Figure 3 a is a range time where occurs a PVC. Figure 3 b presents the wavelet coefficients for this range time. It can be observed that larger variations are observed on the scales 3 (ω_{3}) and 4 (ω _{4}), but during the PVC a larger variations are observed on the scales 4 (ω_{4}), 5 (ω_{5} ) and 6 (ω_{6}), principally the coefficients in the scale 5 (ω_{5}). It can be verified that when a PVC occurs the wavelet coefficients increase, if compared to normal heartbeat wavelet coefficients.
Algorithm results based on db2 mother wavelet for record 100 analysis: (a) is the ECG signal interval that occurs a PVC; (b) is the wavelet coefficients in the six resolution levels (ω1, ω2, ω3, ω4, ω5 and ω6); (c) wavelet coefficients energy on all scales.
The largest variation observed on wavelet coefficients at scale 5 (ω _{5}) implies that the highest energy portion is on the scale 5. Figure 3 c illustrates the wavelet coefficients energy on the six resolutions levels. It can be verified that the energy increases enough when the PVC occurs, and this event can indicate a PVC occurrence. The energies values increase in all resolution levels, but in last three levels are most significant, in specially at level 5 (wavelet coefficients energy ω_{5} ), and associated with threshold methods can detect the PVC occurrence.
Figure 4 shows the algorithm results based on db2 mother wavelet for the record 102 analysis (MITBIH Arrhythmia Database). In this case, there is a change in the ECG signal behavior after the occurrence of the PVC due to the action of a pacemaker ( Figure 4 a), to control the heart rate. Figure 4 b presents the wavelet coefficients energy on all scales (ω1, ω2, ω3, ω4, ω5 and ω6). If compared to Figure 3 , the highest energy portion is concentrated in the 6^{th} scale, but the energies are also most significant on last two scale. So the detection can occur in any scale or more than one, and the threshold technical provides good comparative analysis for all resolution level.
Algorithm results based on db2 for record 102 analysis: (a) is the ECG signal interval that present a PVC occurrence; (b) presents the wavelet coefficients energy in the six resolution levels (ω1, ω2, ω3, ω4, ω5 and ω6).
Table 3 presents the algorithm comparative results on the following mother wavelets: db2, db4, coif6 and sym4. The table shows the Sensitivity (Se), Positive Predictivity (P+) and Specificity (Sp) parameters used for PVC detection performance comparison.
PVC detection performance comparison on several mother wavelets: db2, db4, coif6 and sym4. Where Se is the Sensitivity value, P^{+} the Positive Predictivity value and Sp the Specificity value.
Table 4 presents the system analysis based on db2 for 36 records from MITBIH Arrhythmia Database, on 80.872 annotated beats, being 3.408 annotated PVC beats. The table shows besides the PVC detected for each data record, the True Positive (TP) and True Negative (TN) value, the False Positive (FP) and False Negative (FN) value, and amount of failures.
PVC detection performance on the MITBIH Arrhythmia Database for db2 mother wavelet: each data record number represents the respective record on the database. The column Total Beats show the annotated beats number in each data record. The Total PVC column indicates the number PVC occurrence in the each data record. The TP and TN are the True Positive and True Negative value, respectively. The FP is the False Positive value and FN is the False Negative value. The columns Failed Detection shows the error detection algorithm in absolute and perceptual value, respectively.
Table 5 lists the processing speed analysis for each analyzed mother wavelet (db2, db4, coif6 and sym4) taking into account a halfhour record from MITBIH Arrhythmia Database. The processing time is computed in seconds.
PVC detection speed performance comparison on the following mother wavelets: db2, db4, coif6 and sym4. It was taken into account a halfhour record from MITBIH Arrhythmia Database. The processing time was verified in seconds.
Discussions
ECG analysis is an important issue related to healthcare, especially for telecardioloy applications. In this paper we presented a system based on Redundant Discrete Wavelet Transform (RDWT) associated with adaptive threshold methods for Premature Ventricular Contraction (PVC) detection with realtime approach.
There are several works that use the Wavelet Transform for ECG analysis, and the Wavelet family most used is the Daubechies family, especially the mother Wavelet db4 ( Arrais et al., 2016 Arrais E Jr, Valentim RAM, Brandão GB. Real time QRS detection based on redundant discrete wavelet transform. IEEE Latin Am Trans. 2016; 14(4):16628. http://dx.doi.org/10.1109/TLA.2016.7483498.
http://dx.doi.org/10.1109/TLA.2016.7483...
; Sasikala and Wahidabanu, 2010 Sasikala P, Wahidabanu R. Robust r peak and qrs detection in electrocardiogram using wavelet transform. Inter J of Advan Comp Sci and AppIJACSA. 2010; 1(6):4853. ; Singh and Tiwari, 2006 Singh BN, Tiwari AK. Optimal selection of wavelet basis function applied to ECG signal denoising. Dig Sig Proc. 2006; 16(3):27587. http://dx.doi.org/10.1016/j.dsp.2005.12.003.
http://dx.doi.org/10.1016/j.dsp.2005.12...
). However, is not sure the choice for db4. In this paper was presented a comparative study between three Wavelet families and some of their mother wavelets: Daubechies (db2, db4, db6, db8, and db12), Coiflets (coif6, coif12 and coif18) and Symlets (sym4, sym6, sym8 and sym10). The Table 2 showed the comparative results.
The comparative study was based on standard deviation analysis between the ECG original signal energy and the scaling coefficients energy at all resolution level. It was analyzed around thirty recordings from MITBIH Arrhythmia Database as reference, which presents both ECG signal with and without PVC occurrence. The results showed that the loworder filters provide the best results for ECG analysis. This is a very interesting result, since the numerical processing time is directly proportional to the order filter, so loworder filters require less computational costs time.
It was verified that the best mother wavelet for ECG signal analysis is the db2 (Daubechies family. Furthermore, it can be observed that the Daubechies family provides the best results if compared to Coiflets wavelet family. However, comparing the Daubechies and Symlets family the results were very close, what was expected, since Symlets family is a modified version of Daubechies wavelets with increased symmetry. However, the Symlets family mathematical implementation is more complex if compared to Daubechies family.
It was observed that based on the energy of the wavelet coefficients and threshold methods can detect the occurrence of a premature ventricular contraction. Besides that, the energy wavelet coefficients provide the frequency band where the PVC energy present the most portion and the PVC duration time influence in the heartbeat. Thus, the frequency band can be used as indicative parameter of the ectopic stimulus origin ( Malmivuo and Plonsey, 1995 Malmivuo J, Plonsey R. Bioelectromagnetism: principles and applications of bioelectric and biomagnetic fields. Oxford: Oxford University Press; 1995. http://dx.doi.org/10.1093/acprof:oso/9780195058239.001.0001.
http://dx.doi.org/10.1093/acprof:oso/97...
).
The database chosen for validated the algorithm is one of the most used for this propose. The Sensitivity (Se), Positive Predictivity (P^{+}) and Specificity (Sp) are the essentially parameters should be used to evaluate the performance results of arrhythmia detection algorithms ( Kohler et al., 2002 Kohler BU, Hennig C, Orglmeister R. The principles of software QRS detection. IEEE Eng Med Biol Mag. 2002; 21(1):4257. http://dx.doi.org/10.1109/51.993193. PMid:11935987.
http://dx.doi.org/10.1109/51.993193 ...
; Martinez et al., 2004 Martinez J, Almeida R, Olmos S, Rocha A, Laguna P. A waveletbased ecg delineator: evaluation on standard databases. IEEE Trans Biomed Eng. 2004; 51(4):57081. http://dx.doi.org/10.1109/TBME.2003.821031.
http://dx.doi.org/10.1109/TBME.2003.821...
; Wang, 2013 Wang J. Proposed new requirements for testing and reporting performance results of arrhythmia detection algorithms. In: Computing in Cardiology; 2013 Sept 2225; Zaragoza, Spain. USA: IEEE; 2013. p. 96770. ). The Sensitivity (Se) indicates the algorithm’s ability to detect truly positive characteristics, therefore high Sensitivity indicates few false negative cases. The Positive Predictivity Value (P^{+}) indicates the algorithm’s ability to detect positive characteristics that are really positive, so the lower number of false positives provides the better algorithm positive predictability. The Specificity (Sp) indicates the algorithm’s ability to detect negative characteristics, therefore high Specificity indicates few false positive cases.
In general, Sensitivity and Specificity are the most indicated parameters for overall accuracy algorithm, whereas Sensitivity and Positive Predictivity Values are the indicated for algorithm performance measures ( Wang, 2013 Wang J. Proposed new requirements for testing and reporting performance results of arrhythmia detection algorithms. In: Computing in Cardiology; 2013 Sept 2225; Zaragoza, Spain. USA: IEEE; 2013. p. 96770. ). Therefore, based on these results it was found that there is a tradeoff between the choice of wavelet filter order and the performance parameters. The high order wavelet filter presents a higher Sensitivity and Specificity if compared to low order filter, as verified between db2 and db4. Whereas the Positive Predictivity Value presents a high value for low order filter and low value for high order wavelet filter.
Although the db2 and db4 performance have been very close ( Table 3 ), it was chosen the db2 for proposed system, in order to achieve the best tradeoff, with good Sensitivity, Positive Predictivity Value, Specificity and low order wavelet filter implementation algorithm. Through the Table 5 can verified that db2 presents the best speed performance. So, the db2 mother wavelet is the most indicated mother wavelet that provides reliable and accurate detection of the ECG signal characteristic.
Acknowledgements
The authors would like to thank the Brazilian National Research Council (CNPq), the Federal University of Rio Grande do Norte and the Rural Federal University of SemiArid for the support throughout the work.

How to cite this article: Arrais Junior E, Valentim RAM, Brandão GB. Realtime premature ventricular contractions detection based on Redundant Discrete Wavelet Transform. Res Biomed Eng. 2018; 34(2):pppp. DOI: 10.1590/24464740.01618.
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Publication Dates

Publication in this collection
26 July 2018 
Date of issue
JulSep 2018
History

Received
28 Feb 2018 
Accepted
14 June 2018