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A unified non-linear approach based on recurrence quantification analysis and approximate entropy: application to the classification of heart rate variability of age-stratified subjects

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Abstract

This paper presents a unified approach based on the recurrence quantification analysis (RQA) and approximate entropy (ApEn) for the classification of heart rate variability (HRV). In this paper, the optimum tolerance threshold (ropt) corresponding to ApEnmax has been used for RQA calculation. The experimental data length (N) of RR interval series (RRi) is optimized by taking ropt as key parameter. ropt is found to be lying within the recommended range of 0.1 to 0.25 times the standard deviation of the RRi, when N ≥ 300. Consequently, RQA is applied to the age stratified RRi and indices such as percentage recurrence (%REC), percentage laminarity (%LAM), and percentage determinism (%DET) are calculated along with ApEnmax, \( {\mathrm{r}}_{\mathrm{opt}}^{\mathrm{min}} \), \( {\mathrm{r}}_{\mathrm{opt}}^{\mathrm{max}} \), and an index namely the radius differential (RD). Certain standard HRV statistical indices such as mean RR, standard deviation of RR (or NN) interval (SDNN), and the square root of the mean squared differences of successive RR intervals (RMSSD) (Eur Hear J 17:354–381, 1996) are also found for comparison. It is observed that (i) RD can discriminate between the elderly and young subjects with a value of 0.1151 ± 0.0236 (mean ± SD) and 0.0533 ± 0.0133 (mean ± SD) respectively for the elderly and young subjects and is found to be statistically significant with p < 0.05. (ii) Similar significant discrimination was obtained using \( {\mathrm{r}}_{\mathrm{opt}}^{\mathrm{min}} \) with a value of 0.1827 ± 0.0382 (mean ± SD) and 0.2248 ± 0.0320 (mean ± SD) (iii) other significant indices were found to be %REC, %DET, %LAM, SDNN, and RMSSD; however, ApEnmax was found to be insignificant with p > 0.05. The above features of RRi time series were tested for classification using support vector machine (SVM) and multilayer perceptron neural network (MLPNN). Higher classification accuracy was achieved using SVM with a maximum value of 99.71%.

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References

  1. Guidelines (1996) Guidelines Heart rate variability. Eur Hear J 17:354–381. https://doi.org/10.1161/01.CIR.93.5.1043

    Article  Google Scholar 

  2. Acharya UR, Joseph KP, Kannathal N et al (2006) Heart rate variability: a review. Med Biol Eng Comput 44:1031–1051. https://doi.org/10.1007/s11517-006-0119-0

    Article  Google Scholar 

  3. Sassi R, Cerutti S, Lombardi F, Malik M, Huikuri HV, Peng CK, Schmidt G, Yamamoto Y, Document Reviewers, Gorenek B, Lip GYH, Grassi G, Kudaiberdieva G, Fisher JP, Zabel M, Macfadyen R (2015) Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society. Europace 17:1341–1353. https://doi.org/10.1093/europace/euv015

    Article  PubMed  Google Scholar 

  4. Kaplan DT, Furman MI, Pincus SM, Ryan SM, Lipsitz LA, Goldberger AL (1991) Aging and the complexity of cardiovascular dynamics. Biophys J 59:945–949. https://doi.org/10.1016/S0006-3495(91)82309-8

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  5. Li X, Yu S, Chen H, Lu C, Zhang K, Li F (2015) Cardiovascular autonomic function analysis using approximate entropy from 24-h heart rate variability and its frequency components in patients with type 2 diabetes. J Diabetes Investig 6:227–235. https://doi.org/10.1111/jdi.12270

    Article  PubMed  Google Scholar 

  6. Singh A, Saini BS, Singh D (2016) A new baroreflex sensitivity index based on improved Hilbert-Huang transform for assessment of baroreflex in supine and standing postures. Biocybern Biomed Eng 36:355–365. https://doi.org/10.1016/j.bbe.2016.01.006

    Article  Google Scholar 

  7. Shiogai Y, Stefanovska A, McClintock PVEE (2010) Nonlinear dynamics of cardiovascular ageing. Phys Rep 488:51–110. https://doi.org/10.1016/j.physrep.2009.12.003

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  8. Javorka M, Trunkvalterova Z, Tonhajzerova I, Javorkova J, Javorka K, Baumert M (2008) Short-term heart rate complexity is reduced in patients with type 1 diabetes mellitus. Clin Neurophysiol 119:1071–1081. https://doi.org/10.1016/j.clinph.2007.12.017

    Article  PubMed  Google Scholar 

  9. Castiglioni P, Parati G, Di Rienzo M et al (2011) Scale exponents of blood pressure and heart rate during autonomic blockade as assessed by detrended fluctuation analysis. J Physiol 589:355–369. https://doi.org/10.1113/jphysiol.2010.196428

    Article  PubMed  CAS  Google Scholar 

  10. Tulppo MP, Mäkikallio TH, Seppänen T et al (2001) Effects of pharmacological adrenergic and vagal modulation on fractal heart rate dynamics. Clin Physiol 21:515–523. https://doi.org/10.1046/j.1365-2281.2001.00344.x

    Article  PubMed  CAS  Google Scholar 

  11. Singh A, Saini BS, Singh D (2015) Multiscale joint symbolic transfer entropy for quantification of causal interactions between heart rate and blood pressure variability under postural stress. Fluct Noise Lett 14:1550031. https://doi.org/10.1142/S0219477515500315

    Article  Google Scholar 

  12. Catai AM, Takahashi ACM, Perseguini NM, Milan J, Minatel V, Rehder-Santos P, Marchi A, Bari V, Porta A (2014) Effect of the postural challenge on the dependence of the cardiovascular control complexity on age. Entropy 16:6686–6704. https://doi.org/10.3390/e16126686

    Article  Google Scholar 

  13. Orini M, Laguna P, Mainardi L, et al (2011) Characterization of the dynamic interactions between cardiovascular signals by cross time-frequency analysis: phase differences, time delay and phase locking. In: International Conference on Numerical Method in Engineering

  14. Orini M, Laguna P, Mainardi LT, Bailón R (2012) Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time-frequency analysis. Physiol Meas 33:315–331. https://doi.org/10.1088/0967-3334/33/3/315

    Article  PubMed  CAS  Google Scholar 

  15. Watanabe E, Kiyono K, Hayano J, Yamamoto Y, Inamasu J, Yamamoto M, Ichikawa T, Sobue Y, Harada M, Ozaki Y (2015) Multiscale entropy of the heart rate variability for the prediction of an ischemic stroke in patients with permanent atrial fibrillation. PLoS One 10:1–13. https://doi.org/10.1371/journal.pone.0137144

    Article  CAS  Google Scholar 

  16. Akselrod S, Gordon D, Ubel F et al (1981) Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science (80- ) 213:220–222. https://doi.org/10.1126/science.6166045

    Article  CAS  Google Scholar 

  17. Orini M, Bailon R, Mainardi LT, Laguna P, Flandrin P (2012) Characterization of dynamic interactions between cardiovascular signals by time-frequency coherence. IEEE Trans Biomed Eng 59:663–673. https://doi.org/10.1109/TBME.2011.2171959

    Article  PubMed  Google Scholar 

  18. Brennan M, Palaniswami M, Kamen P (2001) Do existing measures of Poincareé plot geometry reflect nonlinear features of heart rate variability? IEEE Trans Biomed Eng 48:1342–1347. https://doi.org/10.1109/10.959330

    Article  PubMed  CAS  Google Scholar 

  19. Richman JS, Moorman JR, Yamauchi M et al (2011) Physiological time-series analysis using approximate entropy and sample entropy. Cardiovasc Res:2039–2049

  20. Lake DE (2006) Renyi entropy measures of heart rate Gaussianity. IEEE Trans Biomed Eng 53:21–27. https://doi.org/10.1109/TBME.2005.859782

    Article  PubMed  Google Scholar 

  21. Voss A, Schulz S, Schroeder R, Baumert M, Caminal P (2009) Methods derived from nonlinear dynamics for analysing heart rate variability. Philos Trans R Soc A Math Phys Eng Sci 367:277–296. https://doi.org/10.1098/rsta.2008.0232

    Article  Google Scholar 

  22. Rawal K, Saini BS, Saini I (2015) Adaptive correlation dimension method for analysing heart rate variability during the menstrual cycle. Australas Phys Eng Sci Med 38:509–523. https://doi.org/10.1007/s13246-015-0369-y

    Article  PubMed  Google Scholar 

  23. Arcentales A, Giraldo BF, Caminal P, et al (2011) Recurrence quantification analysis of heart rate variability and respiratory flow series in patients on weaning trials. 2011 Annu Int Conf IEEE Eng Med Biol Soc 2724–2727 . https://doi.org/10.1109/IEMBS.2011.6090747

  24. Beckers F (2006) Aging and nonlinear heart rate control in a healthy population. Am J Physiol Heart Circ Physiol 290:H2560–H2570. https://doi.org/10.1152/ajpheart.00903.2005

    Article  PubMed  CAS  Google Scholar 

  25. Iyengar N, Peng CK, Morin R et al (1996) Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am J Phys 271:R1078–R1084

    CAS  Google Scholar 

  26. Kampouraki A, Manis G, Nikou C (2009) Heartbeat time series classification with support vector machines. IEEE Trans Inf Technol Biomed 13:512–518. https://doi.org/10.1109/TITB.2008.2003323

    Article  PubMed  Google Scholar 

  27. Manikandan MS, Soman KP (2012) A novel method for detecting R-peaks in electrocardiogram (ECG) signal. Biomed Signal Process Control 7:118–128. https://doi.org/10.1016/j.bspc.2011.03.004

    Article  Google Scholar 

  28. Singh A, Saini BS, Singh D (2016) An alternative approach to approximate entropy threshold value (r) selection: application to heart rate variability and systolic blood pressure variability under postural challenge. Med Biol Eng Comput 54:723–732. https://doi.org/10.1007/s11517-015-1362-z

    Article  PubMed  CAS  Google Scholar 

  29. Webber CL, Zbilut JP (2005) Recurrence quantification analysis of nonlinear dynamical systems. In: Riley M, Van Orden G (eds.) Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences (pp. 26–94). USA: National Science Foundation

  30. Webber CL, Marwan N (2015) Recurrence Quantification Analysis: Theory and Best Practices, 1st ed. Springer International Publishing

  31. Orhan U, Hekim M, Ozer M (2011) EEG signals classification using the K-means clustering and a multilayer perceptron neural network model. Expert Syst Appl 38:13475–13481. https://doi.org/10.1016/j.eswa.2011.04.149

    Article  Google Scholar 

  32. Subasi A (2005) Automatic recognition of alertness level from EEG by using neural network and wavelet coefficients. Expert Syst Appl 28:701–711. https://doi.org/10.1016/j.eswa.2004.12.027

    Article  Google Scholar 

  33. Oğulata SN, Şahin C, Erol R (2009) Neural network-based computer-aided diagnosis in classification of primary generalized epilepsy by EEG signals. J Med Syst 33:107–112. https://doi.org/10.1007/s10916-008-9170-8

    Article  PubMed  Google Scholar 

  34. Hazarika N, Chen JZ, Tsoi AC, Sergejew A (1997) Classification of EEG signals using the wavelet transform. Proc 13th Int Conf Digit Signal Process 1:61–72 . https://doi.org/10.1016/S0165-1684(97)00038-8

  35. Lee H, Shin S-Y, Seo M, Nam GB, Joo S (2016) Prediction of ventricular tachycardia one hour before occurrence using artificial neural networks. Sci Rep 6:32390. https://doi.org/10.1038/srep32390

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  36. Jan SU, Lee Y-D, Shin J, Koo I (2017) Sensor fault classification based on support vector machine and statistical time-domain features. IEEE Access 5:8682–8690. https://doi.org/10.1109/ACCESS.2017.2705644

    Article  Google Scholar 

  37. Zhang L, Xiong G, Liu H, Zou H, Guo W (2010) Applying improved multi-scale entropy and support vector machines for bearing health condition identification. Proc Inst Mech Eng Part C J Mech Eng Sci 224:1315–1325. https://doi.org/10.1243/09544062JMES1784

    Article  Google Scholar 

  38. Babaoglu İ, Findik O, Ülker E (2010) A comparison of feature selection models utilizing binary particle swarm optimization and genetic algorithm in determining coronary artery disease using support vector machine. Expert Syst Appl 37:3177–3183. https://doi.org/10.1016/j.eswa.2009.09.064

    Article  Google Scholar 

  39. Porta A, Catai AM, Takahashi ACM, Magagnin V, Bassani T, Tobaldini E, van de Borne P, Montano N (2011) Causal relationships between heart period and systolic arterial pressure during graded head-up tilt. Am J Physiol Regul Integr Comp Physiol 300:R378–R386. https://doi.org/10.1152/ajpregu.00553.2010

    Article  PubMed  CAS  Google Scholar 

  40. Schinkel S, Dimigen O, Marwan N (2008) Selection of recurrence threshold for signal detection. Eur Phys J Spec Top 164:45–53. https://doi.org/10.1140/epjst/e2008-00833-5

    Article  Google Scholar 

  41. Lu S, Chen X, Kanters JK et al (2008) Automatic selection of the threshold value r for approximate entropy. IEEE Trans Biomed Eng 55:1966–1972. https://doi.org/10.1109/TBME.2008.919870

    Article  PubMed  Google Scholar 

  42. Chon K, Scully C, Lu S (2009) Approximate entropy for all signals. IEEE Eng Med Biol Mag 28:18–23. https://doi.org/10.1109/MEMB.2009.934629

    Article  PubMed  Google Scholar 

  43. Ding H, Crozier S, Wilson S (2007) A new heart rate variability analysis method by means of quantifying the variation of nonlinear dynamic patterns. IEEE Trans Biomed Eng 54:1590–1597. https://doi.org/10.1109/TBME.2007.893495

    Article  PubMed  Google Scholar 

  44. García-González MA, Fernández-Chimeno M, Ramos-Castro J (2009) Errors in the estimation of approximate entropy and other recurrence-plot-derived indices due to the finite resolution of RR time series. IEEE Trans Biomed Eng 56:345–351. https://doi.org/10.1109/TBME.2008.2005951

    Article  PubMed  Google Scholar 

  45. Pincus SM (1991) Approximate entropy as a measure of system complexity. Proc Natl Acad Sci 88:2297–2301. https://doi.org/10.1073/pnas.88.6.2297

    Article  PubMed  CAS  Google Scholar 

  46. Daskalov I, Christov I (1997) Improvement of resolution in measurement of electrocardiogram RR intervals by interpolation. Med Eng Phys 19:375–379. https://doi.org/10.1016/S1350-4533(96)00067-7

    Article  PubMed  CAS  Google Scholar 

  47. Voss A, Heitmann A, Schroeder R, Peters A, Perz S (2012) Short-term heart rate variability—age dependence in healthy subjects. Physiol Meas 33:1289–1311. https://doi.org/10.1088/0967-3334/33/8/1289

    Article  PubMed  CAS  Google Scholar 

  48. Schipke JD, Pelzer M, Arnold G (1999) Effect of respiration rate on short-term heart rate variability. J Clin Basic Cardiol 2:92–95. https://doi.org/10.1161/01.CIR.93.5.1043

    Article  Google Scholar 

  49. Voss A, Schroeder R, Fischer C, et al (2013) Influence of age and gender on complexity measures for short term heart rate variability analysis in healthy subjects. 35th Annu Int Conf IEEE 5574–5577 . https://doi.org/10.1109/EMBC.2013.6610813

  50. Accardo A, D’Addio G, Maestri R, et al (2015) Fractal dimension and power-law behavior reproducibility and correlation in chronic heart failure patients. Eur Signal Process Conf 2015–March

  51. Weippert M, Behrens M, Rieger A, Behrens K (2014) Sample entropy and traditional measures of heart rate dynamics reveal different modes of cardiovascular control during low intensity exercise. Entropy 16:5698–5711. https://doi.org/10.3390/e16115698

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, I K G Punjab Technical University, Jalandhar, Punjab, India

    Vikramjit Singh & Amit Gupta

  2. Ludhiana College of Engineering and Technology, Ludhiana, Punjab, India

    J. S. Sohal

  3. Department of Electrical Engineering, I K G Punjab Technical University, Jalandhar, Punjab, India

    Amritpal Singh

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  1. Vikramjit Singh
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Correspondence to Vikramjit Singh.

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The study abides by the ethical standards and was approved by the research advisory committee of the Inder Kumar Gujral Punjab Technical University, Punjab, India, and informed permission was obtained from all the subjects.

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Singh, V., Gupta, A., Sohal, J.S. et al. A unified non-linear approach based on recurrence quantification analysis and approximate entropy: application to the classification of heart rate variability of age-stratified subjects. Med Biol Eng Comput 57, 741–755 (2019). https://doi.org/10.1007/s11517-018-1914-0

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