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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Calculation Methods in Heart Rate Variability

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 849--861 | DOI:10.5890/DNC.2023.12.010

Amin Gasmi

Societe Francophone de Nutritherapie et de Nutrigenetique Appliquee, Villeurbanne, France

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Abstract

A healthy human body depicts variability to a large extent that can be easily described by using statistical algorithms. If this fluctuation arises occur in normal cycle of the heartbeat, it is called as heart rate variability (HRV). The rhythms of a normal and healthy heart continue to change every second with the metabolic activity that provides the heart and brain a new chance for changing and maintaining homeostasis according to variability. The aim of this research is to study long-term, short-term, and very short-term regulations of the body to cope with the condition of the heart as HRV changes. Time domain, frequency domain, non --linear dynamics are being overviewed. Where time-domain shows HRV changes during a time period of three minutes to one hour, frequency domain parameters illustrate the variation of data over an extended period of time. Nonlinear dynamics provides quantitative measurement of probability and biasedness in values obtained from the electrocardiograph. After careful investigation, it became clear as fact that short term i.e., mechanisms which are as less as five minutes and long term that are about one day cannot be correlated and can't be changed into one another. Moreover, the use of these statistical mechanics in clinical laboratories and therapeutics against myocardial infarction, blood pressure, and diabetes are elucidated in detail to gain access to potential generated by them during heart rate (HR) analysis to control morbidity rate effectively.

References

  1. [1]  Northam, E.A., Rankins, D., Lin, A., Wellard, R.M., Pell, G.S., Finch, S.J., Werther, G.A., and Cameron, F.J. (2009), Central nervous system function in youth with type 1 diabetes 12 years after disease onset, Diabetes Care, 32(3), 445-450.
  2. [2]  Vinik, A.I., Erbas, T., and Casellini, C.M. (2013), Diabetic cardiac autonomic neuropathy, inflammation and cardiovascular disease, Journal of Diabetes Investigation, 4(1), 4-18.
  3. [3]  Schneider, U., Bode, F., Schmidt, A., Nowack, S., Rudolph, A., Doelcker, E.M., Schlattmann, P., Götz, T., and Hoyer, D. (2018), Developmental milestones of the autonomic nervous system revealed via longitudinal monitoring of fetal heart rate variability, Plos One, 13(7), e0200799.
  4. [4]  Visnovcova, Z., Mestanik, M., Javorka, M., Mokra, D., Gala, M., Jurko, A., et al. (2014), Complexity and time asymmetry of heart rate variability are altered in acute mental stress, Physiological Measurement, 35(7), 1319.
  5. [5]  Cygankiewicz, I. and Zareba, W. (2013), Heart rate variability, Handbook of Clinical Neurology, 117(2013), 379-393.
  6. [6]  Tarvainen, M.P., Niskanen, J.-P., Lipponen, J.A., Ranta-Aho, P.O., and Karjalainen, P.A. (2014), Kubios HRV--heart rate variability analysis software, Computer Methods and Programs in Biomedicine, 113(1), 210-220.
  7. [7]  Aysin, B. and Aysin, E. (2006), Effect of respiration in heart rate variability (HRV) analysis, in 2006 International Conference of the IEEE Engineering in Medicine and Biology Society, 1776-1779.
  8. [8]  Brennan, M., Palaniswami, M., and Kamen, P. (2001), Do existing measures of Poincare plot geometry reflect nonlinear features of heart rate variability?, IEEE Transactions on Biomedical Engineering, 48(11), 1342-1347.
  9. [9]  Xhyheri, B., Manfrini, O., Mazzolini, M., Pizzi, C., and Bugiardini, R. (2012), Heart rate variability today, Progress in Cardiovascular Diseases, 55(3), 321-331.
  10. [10]  Salahuddin, L., Cho, J., Jeong, M.G., and Kim, D. (2007), Ultra short term analysis of heart rate variability for monitoring mental stress in mobile settings, in 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 4656-4659.
  11. [11]  Zhang, J. (2007), Effect of age and sex on heart rate variability in healthy subjects, Journal of Manipulative and Physiological Therapeutics, 30(5), 374-379.
  12. [12]  Acharya, U.R., Joseph, K.P., Kannathal, N., Lim, C.M., and Suri, J.S. (2006), Heart rate variability: a review, Medical and Biological Engineering and Computing, 44(12), 1031-1051.
  13. [13]  Moss, D. (2004), Heart rate variability (HRV) biofeedback, Psychophysiology Today, 1(1), 4-11.
  14. [14]  Tyagi, A. and Cohen, M. (2016), Yoga and heart rate variability: A comprehensive review of the literature, International Journal of Yoga, 9(2), 97.
  15. [15]  Mueck-Weymann, M., Janshoff, G., and Mueck, H. (2004), Stretching increases heart rate variability in healthy athletes complaining about limited muscular flexibility, Clinical Autonomic Research, 14(1), 15-18.
  16. [16]  Liu, P.-Y., Tsai, W.-C., Lin, L.-J., Li, Y.-H., Chao, T.-H., Tsai, L.-M., et al. (2003), Time domain heart rate variability as a predictor of long-term prognosis after acute myocardial infarction, Journal of the Formosan Medical Association, 102(7), 474-479.
  17. [17]  Pitzalis, M.V., Mastropasqua, F., Massari, F., Forleo, C., Di Maggio, M., Passantino, A., et al. (1996), Short-and long-term reproducibility of time and frequency domain heart rate variability measurements in normal subjects, Cardiovascular Research, 32(2), 226-233.
  18. [18]  Plews, D.J., Laursen, P.B., Kilding, A.E., and Buchheit, M. (2013), Evaluating training adaptation with heart-rate measures: a methodological comparison, International Journal of Sports Physiology and Performance, 8(6), 688-691.
  19. [19]  Oliveira, M.S., Muzzi, R.A.L., Ara{u}jo, R.B., Muzzi, L.A.L., Ferreira, D.F., Nogueira, R., et al. (2012), Heart rate variability parameters of myxomatous mitral valve disease in dogs with and without heart failure obtained using 24-hour Holter electrocardiography, Veterinary Record, 170(24), 622-622.
  20. [20]  Huber, R., Wojtkowski, M., Taira, K., Fujimoto, J.G., and Hsu, K. (2005), Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles, Optics Express, 13(9), 3513-3528.
  21. [21]  Ryu, K., Sahadevan, J., Khrestian, C.M., Stambler, B.S., and Waldo, A.L. (2006), Use of Fast Fourier Transform Analysis of Atrial Electrograms for Rapid Characterization of Atrial Activation---Implications for Delineating Possible Mechanisms of Atrial Tachyarrhythmias, Journal of Cardiovascular Electrophysiology, 17(2), 198-206.
  22. [22]  Pantoni, C.B.F., Mendes, R.G., Di Thommazo-Luporini, L., Sim\~{o}es, R.P., Amaral-Neto, O., Arena, R., et al. (2014), Recovery of linear and nonlinear heart rate dynamics after coronary artery bypass grafting surgery, Clinical Physiology and Functional Imaging, 34(6), 449-456.
  23. [23]  Wiklund, U., H\"{o}rnsten, R., Karlsson, M., Suhr, O.B., and Jensen, S.M. (2008), Abnormal heart rate variability and subtle atrial arrhythmia in patients with familial amyloidotic polyneuropathy, Annals of Noninvasive Electrocardiology, 13(3), 249-256.
  24. [24]  Castiglioni, P., Parati, G., Di Rienzo, M., Carabalona, R., Cividjian, A., and Quintin, L. (2011), Scale exponents of blood pressure and heart rate during autonomic blockade as assessed by detrended fluctuation analysis, The Journal of Physiology, 589(2), 355-369.
  25. [25]  Fujiwara, Y., Asakura, Y., Shibata, Y., Nishiwaki, K., and Komatsu, T. (2006), A marked decrease in heart rate variability associated with junctional rhythm during anesthesia with sevoflurane and fentanyl, Acta Anaesthesiologica Scandinavica, 50(4), 509-511.
  26. [26]  Kudat, H., Akkaya, V., Sozen, A., Salman, S., Demirel, S., Ozcan, M., et al. (2006), Heart rate variability in diabetes patients, Journal of International Medical Research, 34(3), 291-296.
  27. [27]  Griffin, M.P., Scollan, D.F., and Moorman, J.R. (1994), The dynamic range of neonatal heart rate variability, Journal of Cardiovascular Electrophysiology, 5(2), 112-124.
  28. [28]  Roche, F., Pichot, V., Sforza, E., Duverney, D., Costes, F., Garet, M., et al. (2003), Predicting sleep apnoea syndrome from heart period: a time-frequency wavelet analysis, European Respiratory Journal, 22(6), 937-942.
  29. [29]  Tamura, K., Tsuji, H., Nishiue, T., Yajima, I., Higashi, T., and Iwasaka, T. (1998), Determinants of heart rate variability in chronic hemodialysis patients, American Journal of Kidney Diseases, 31(4), 602-606.
  30. [30]  Wang, H.-M. and Huang, S.-C. (2012), SDNN/RMSSD as a surrogate for LF/HF: a revised investigation, Modelling and Simulation in Engineering, 2012.
  31. [31]  Bilchick, K.C., Fetics, B., Djoukeng, R., Fisher, S.G., Fletcher, R.D., Singh, S.N., et al. (2002), Prognostic value of heart rate variability in chronic congestive heart failure (Veterans Affairs' Survival Trial of Antiarrhythmic Therapy in Congestive Heart Failure), The American Journal of Cardiology, 90(1), 24-28.
  32. [32]  Musialik-{\L}ydka, A., {S}redniawa, B., and Pasyk, S. (2003), Heart rate variability in heart failure, Kardiologia Polska (Polish Heart Journal), 58(1), 14-16.
  33. [33]  Fei, L., Copie, X., Malik, M., and Camm, A.J. (1996), Short-and long-term assessment of heart rate variability for risk stratification after acute myocardial infarction, The American journal of cardiology, 77(9), 681-684.
  34. [34]  Munoz, M.L., Van Roon, A., Riese, H., Thio, C., Oostenbroek, E., Westrik, I., et al. (2015), Validity of (ultra-) short recordings for heart rate variability measurements, PloS one, 10(9), p.e0138921.
  35. [35]  Berntson, G.G., Lozano, D.L., and Chen, Y.J. (2005), Filter properties of root mean square successive difference (RMSSD) for heart rate, Psychophysiology, 42(2), 246-252.
  36. [36]  Ciccone, A.B., Siedlik, J.A., Wecht, J.M., Deckert, J.A., Nguyen, N.D. and Weir, J.P. (2017), Reminder: RMSSD and SD1 are identical heart rate variability metrics, Muscle \& nerve, 56(4), 674-678.
  37. [37]  Erdogan, A., Coch, M., Bilgin, M., Parahuleva, M., Tillmanns, H., Waldecker, B., et al. (2008), Prognostic value of heart rate variability after acute myocardial infarction in the era of immediate reperfusion, Herzschrittmachertherapie+ Elektrophysiologie, 19(4), 161-168.
  38. [38]  Motoki, M., Koakutsu, S. and Hirata, H. (2005), A pulse neural network incorporating short term synaptic plasticity for engineering applications. in Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, 2005, 177-182. The ISCIE Symposium on Stochastic Systems Theory and Its Applications.
  39. [39]  Cai, M. and Davis, R.W. (1990), Yeast centromere binding protein CBF1, of the helix-loop-helix protein family, is required for chromosome stability and methionine prototrophy, Cell, 61(3), 437-446.
  40. [40]  Madrid, A.H., Mestre, J.L., Moro, C., Vivas, E., Tejero, I., Novo, L., et al. (1995), Heart rate variability and inappropriate sinus tachycardia after catheter ablation of supraventricular tachycardia, European Heart Journal, 16(11) 1637-1640.
  41. [41]  Zabel, M., Klingenheben, T. and Hohnloser, S.H. (1994), Changes in Autonomic Tone Following Thrombolytic Therapy for Acute Myocardial Infarction, Journal of Cardiovascular Electrophysiology, 5(3), 211-218.
  42. [42]  Lagana', B., Tubani, L., Maffeo, N., Vella, C., Makk, E., Baratta, L., et al. (1996), Heart rate variability and cardiac autonomic function in systemic lupus erythematosus, Lupus, 5(1), 49-55.
  43. [43]  Nussbaumer, H.J. (1981), The Fast Fourier Transform, in Fast Fourier Transform and Convolution Algorithms, Springer Berlin Heidelberg: Berlin, Heidelberg. 80-111.
  44. [44]  Joze, H.R.V. and Drew, M.S. (2013), Exemplar-based color constancy and multiple illumination, IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(5), 860-873.
  45. [45]  Sarty, G.E., Bennett, R., and Cox, R.W. (2001), Direct reconstruction of non-Cartesian k-space data using a nonuniform fast Fourier transform, Magnetic Resonance in Medicine, 45(5), 908-915.
  46. [46]  Lu, Z., Scherlag, B.J., Lin, J., Niu, G., Ghias, M., Jackman, W.M., et al. (2008), Autonomic Mechanism for Complex Fractionated Atrial Electrograms: Evidence by Fast Fourier Transform Analysis, Journal of Cardiovascular Electrophysiology, 19(8), 835-842.
  47. [47]  Nguyen, T.H., Zhou, H.-X., and Minh, D.D.L. (2018), Using the fast fourier transform in binding free energy calculations, Journal of Computational Chemistry, 39(11), 621-636.
  48. [48]  Wang, L.L., Fang, D.G., and Sheng, W.X. (2003), Combination of genetic algorithm (GA) and fast fourier transform (FFT) for synthesis of arrays, Microwave and Optical Technology Letters, 37(1), 56-59.
  49. [49]  Kawahito, S., Nakata, K.-i., Nonaka, K., Sato, T., Yoshikawa, M., Takano, T., et al. (2000), Analysis of the Arterial Blood Pressure Waveform Using Fast Fourier Transform Technique During Left Ventricular Nonpulsatile Assistance: In Vitro Study, Artificial Organs, 24(7), 580-583.
  50. [50]  Platisa, M.M., Nestorovic, Z., Damjanovic, S., and Gal, V. (2006), Linear and non-linear heart rate variability measures in chronic and acute phase of anorexia nervosa, Clinical Physiology and Functional Imaging, 26(1), 54-60.
  51. [51]  Goldberger, A.L. and West, B.J. (1987), Applications of Nonlinear dynamics to clinical cardiologya, Annals of the New York Academy of Sciences, 504(1), 195-213.
  52. [52]  Mourot, L., Bouhaddi, M., Perrey, S., Cappelle, S., Henriet, M.-T., Wolf, J.-P., et al. (2004), Decrease in heart rate variability with overtraining: assessment by the Poincar{e} plot analysis, Clinical Physiology and Functional Imaging, 24(1), 10-18.
  53. [53]  Javorka, M., Javorkov{a}, J., Tonhajzerov{a}, I., Calkovska, A., and Javorka, K. (2005), Heart rate variability in young patients with diabetes mellitus and healthy subjects explored by Poincar{e} and sequence plots, Clinical Physiology and Functional Imaging, 25(2), 119-127.
  54. [54]  De Vito, G., Galloway, S.D.R., Nimmo, M.A., Maas, P., and Mcmurray, J.J.V. (2002), Effects of central sympathetic inhibition on heart rate variability during steady-state exercise in healthy humans, Clinical Physiology and Functional Imaging, 22(1), 32-38.
  55. [55]  Zhang, Q., Xu, C.-Y., Chen, Y.D., and Yu, Z. (2008), Multifractal detrended fluctuation analysis of streamflow series of the Yangtze River basin, China, Hydrological Processes, 22(26), 4997-5003.
  56. [56]  Galaska, R., Makowiec, D., Dudkowska, A., Koprowski, A., Chlebus, K., Wdowczyk-Szulc, J., et al. (2008), Comparison of Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis of Heart Rate in Patients with Systolic Dysfunction of Left Ventricle, Annals of Noninvasive Electrocardiology, 13(2), 155-164.
  57. [57]  Yamanaka, N., Aoyama, T., Ikeda, N., Higashihara, M., and Kamata, K. (2005), Characteristics of heart rate variability entropy and blood pressure during hemodialysis in patients with end-stage renal disease, Hemodialysis International, 9(3), 303-308.
  58. [58]  Qureshi, S. and Jan, R. (2021), Modeling of measles epidemic with optimized fractional order under Caputo differential operator, Chaos, Solitons \& Fractals, 145110766.
  59. [59]  Qureshi, S., Yusuf, A., and Aziz, S. (2021), Fractional numerical dynamics for the logistic population growth model under Conformable Caputo: a case study with real observations, Physica Scripta, 96(11), 114002.
  60. [60]  Yusuf, A., Qureshi, S., Inc, M., Aliyu, A.I., Baleanu, D., and Shaikh, A.A. (2018), Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel, Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(12), 123121.
  61. [61]  Mohammadi, H., Rezapour, S., and Jajarmi, A. (2021), On the fractional SIRD mathematical model and control for the transmission of COVID-19: the first and the second waves of the disease in Iran and Japan, ISA transactions.
  62. [62]  Baleanu, D., Sajjadi, S.S., Jajarmi, A., Defterli, O., Asad, J.H., and Tulkarm, P. (2021), The fractional dynamics of a linear triatomic molecule, Romanian Reports in Physics, 73(1), 105.
  63. [63]  Qureshi, S. (2021), Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform, Journal of Applied Mathematics and Computational Mechanics, 20(1), 83-89.
  64. [64]  Baleanu, D., Zibaei, S., Namjoo, M., and Jajarmi, A. (2021), A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system, Advances in Difference Equations, 2021(1), 1-19.
  65. [65]  Baleanu, D., Sajjadi, S.S., Asad, J.H., Jajarmi, A., and Estiri, E. (2021), Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system, Advances in Difference Equations, 2021(1), 1-24.

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