Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats

Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats

Background/aim: Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of systems such as the cardiorespiratory system. Materials and methods: In this study, we recorded tracheal air flow signals, including PNCG signals, from 3 representative anesthetized rats and analyzed the nonlinear behavior of these complex signals using Lyapunov exponents. Results: Lyapunov exponents may also be used to determine the normal and pathological structure of biological systems. If the signals have at least one positive Lyapunov exponent, the signals reflect chaotic activity, as seen in PNCG signals in rats; the largest Lyapunov exponents of the signals of the healthy rats were greater than zero in this study. Conclusion: A method was proposed to determine the diagnostic and prognostic values of the cardiorespiratory system of rats using the arrangement of the PNCG and Lyapunov exponents, which may be monitored as vitality indicators.

___

  • 1. Goldberger AL, Rigney DR, West BJ. Chaos and fractals in human physiology. Sci Am 1999; 262: 42–49.
  • 2. Reitan JA, Lim A. Automated measurement and frequency analysis of the pneumocardiogram. Anesth Analg 1978; 57: 647–652.
  • 3. Heckman JL, Stewart GH, Tremblay G, Lynch PR. Relationship between stroke volume and pneumocardiogram. J Appl Physiol 1982; 52: 1672–1677.
  • 4. Eckmann JP, Kamphorst SO, Ruelle D, Ciliberto S. Lyapunov exponents from time series. Phys Rev A 1986; 34: 4971–4979.
  • 5. Natarajan K, Acharya UR, Alias F, Tiboleng T, Puthusserypady SK. Nonlinear analysis of EEG signals at different mental states. Biomed Eng Online 2004; 3: 7.
  • 6. Güler NF, Übeyli ED, Güler I. Recurrent neural networks employing Lyapunov exponents for EEG signals classification. Expert Syst Appl 2005; 29: 506–514.
  • 7. Rosenstein M, Collins J, De Luca C. A practical method for calculating largest Lyapunov exponents for small data sets. Physica D 1993; 65: 117–134.
  • 8. Schuster HG. Deterministic Chaos. 2nd ed. Weinheim, Germany: Physik Verlag; 1988.
  • 9. Packard NH, Crutchfield JP, Farmer JD, Shaw RS. Geometry from time series. Phys Rev Lett 1980; 45: 712–716.
  • 10. Andrew M, Fraser H. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986; 33: 1134–1140.
  • 11. Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992; 45: 3403–3411.
  • 12. Wysocki M, Fiamma MN, Straus C, Poon CS, Similowski T. Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration. Resp Physiol Neurobi 2006; 153: 54–65.
  • 13. Caminal P, Domingo L, Giraldo BF, Vallverdu M, Benito S, Vazquez G, Kaplan D. Variability analysis of the respiratory volume based on non-linear prediction methods. Med Biol Eng Comput 2004; 42: 86–91.
  • 14. Schmidt M, Demoule A, Cracco C, Gharbi A, Fiamma MN, Straus C, Duguet A, Gottfried SB, Similowski T. Neurally adjusted ventilatory assist increases respiratory variability and complexity in acute respiratory failure. Anesthesiology 2010; 112: 670–681.
  • 15. Akay M, Sekine N. Investigating the complexity of respiratory patterns during recovery from severe hypoxia. J Neural Eng 2004; 1: 16–20.
  • 16. Samara Z, Raux M, Fiamma MN, Gharbi A, Gottfried SB, Poon CS, Similowski T, Straus C. Effects of inspiratory loading on the chaotic dynamics of ventilatory flow in humans. Resp Physiol Neurobi 2009; 165: 82–89.
  • 17. Varela M, Jimenez L, Farina R. Complexity analysis of the temperature curve: new information from body temperature. Eur J Appl Physiol 2003; 89: 230–237.
  • 18. Gu H, Stein EA, Yang Y. Nonlinear responses of cerebral blood volume, blood flow and blood oxygenation signals during visual stimulation. Magn Reson Imaging 2005; 23: 921–928.
  • 19. Pereda E, Quiroga RQ, Bhattacharya J. Nonlinear multivariate analysis of neurophysiological signals. Prog Neurobiol 2005; 77: 1–37.
  • 20. Erem B, Stovicek P, Brooks DH. Manifold learning for analysis of low-order nonlinear dynamics in high-dimensional electrocardiographic signals. Proc IEEE Int Symp Biomed Imaging 2012; 2012: 844–847.
  • 21. Beckers F, Verheyden B, Aubert AE. Aging and nonlinear heart rate control in a healthy population. Am J Physiol-Heart C 2006; 290: 2560–2570.
  • 22. Zwiener U, Hoyer D, Bauer R, Lüthke B, Walter B, Schmidt K, Hallmeyer S, Kratzsch B, Eiselt M. Deterministic–chaotic and periodic properties of heart rate and arterial pressure fluctuations and their mediation in piglets. Cardiovasc Res 1996; 31: 455–465.
  • 23. Derry G, Derry P. Characterization of chaotic dynamics in the human menstrual cycle. Nonlinear Biomed Phys 2010; 4: 5.
  • 24. Wagner CD, Mrowka R, Nafz B, Persson PB. Complexity and “chaos” in blood pressure after baroreceptor denervation of conscious dogs. Am J Physiol 1995; 269: H1760–H1766.
  • 25. Hampson KM, Mallen EA. Chaos in ocular aberration dynamics of the human eye. Biomed Opt Express 2012; 3: 863– 877.
  • 26. Kannathal N, Puthusserypady SK, Choo Min L. Complex dynamics of epileptic EEG. Conf Proc IEEE Eng Med Biol Soc 2004; 1: 604–607.
  • 27. Khoa TQ, Huong NT, Toi VV. Detecting epileptic seizure from scalp EEG using Lyapunov spectrum. Comput Math Method M 2012; 2010: 847686.
  • 28. Zeren T, Özbek M, Ekerbiçer N, Yalçin GÇ, Akdeniz KG. Sensitively recorded breathing signals of rats and their nonlinear dynamics. J Biochem Bioph Meth 2007; 70: 573–577.
  • 29. Yalcin GC, Akdeniz KG. CLDW physiological  system: as an autonomous complex physical system. In: Proceedings of the School and Conference on Complex Systems and Nonextensive Statistical Mechanics; 31 July–8 August 2006; Trieste, Italy. Trieste, Italy: The Abdus Salam International Centre for Theoretical Physics; 2006. p. 1.
  • 30. Yalcin GC, Akdeniz KG. Lyapunov exponents and chaotic ‘cldw’ physiological system. In: Proceedings of the International Congress Nonlinear Dynamical Analysis; 4–8 June 2007; Saint Petersburg, Russia. p. 352.
  • 31. Uzel S. An application on the time series analysis method. MSc, Yıldız Technical University, İstanbul, Turkey, 2008.
  • 32. Akıllı M. Lyapunov exponents in a chaotic physical system and q-statistics. MSc, İstanbul University, İstanbul, Turkey, 2009.
  • 33. Kreit JW, Sciurba FC. The accuracy of pneumotachograph measurements during mechanical ventilation. Am J Resp Crit Care 1996; 154: 913–917.
  • 34. Reitan JA, Warpinski MA, Martucci RW. Determinants and genesis of canine pneumocardiogram. Anesth Analg 1978; 57: 653–662.
  • 35. Johnson WK. The dynamic pneumocardiogram: an application of coherent signal processing to cardiovascular measurement. IEEE T Bio-Med Eng 1981; 28: 471–475.
  • 36. Bijaoui E, Bocannier PF, Bates JH. Mechanical output impedance of the lung determined from cardiogenic oscillations. J Appl Physiol 2001; 91: 859–865.
  • 37. Wessale JL, Bourland JD, Geddes LA. Relationship between tracheal air flow and induced changes in intrathoracic volume: a basis for calibration of pneumocardiogram. Jpn Heart J 1988; 29: 99–106.
  • 38. Petak F, Babik B, Asztalos T, Hall GL, Deak ZI, Sly PD, Hantos Z. Airway and tissue mechanics in anesthetized paralyzed children. Pediatr Pulm 2003; 35: 169–176.
  • 39. Hegger R, Kantz H, Schreiber T. Practical implementation of nonlinear time series methods: The Tisean Package. Chaos 1999; 9: 413–435.
  • 40. Elder DE, Larsen PD, Campbell AJ, Galletly DC. Cardioventilatory coupling and inter-breath variability in children referred for polysomnography. Resp Physiol Neurobi 2012; 181: 1–7.
  • 41. Sin PY, Webber MR, Galletly DC, Tzeng YC. Relationship between cardioventilatory coupling and pulmonary gas exchange. Clin Physiol Funct I 2012; 32: 476–480.
  • 42. Otero-Siliceo E, Arriada-Mendicoa N. Is it healthy to be chaotic? Med Hypotheses 2003; 60: 233–236.
  • 43. Babloyantz A, Destexhe A. Low dimensional chaos is an instance of epilepsy. P Natl Acad Sci USA 1986; 83: 3513–3517.
  • 44. Babloyantz A, Destexhe A. Is the normal heart a periodic oscillator? Biol Cybern 1988; 58: 203–211.
  • 45. Sassi R, Signorini MG, Cerutti S. Multifractality and heart rate variability. Chaos 2009; 19: 028507.
  • 46. Perkiömäki JS, Mäkikallio TH, Huikuri HV. Fractal and complexity measures of heart rate variability. Clin Exp Hypertens 2005; 277: 149–158.
  • 47. Huikuri HV, Perkiömäki JS, Maestri R, Pinna GD. Clinical impact of evaluation of cardiovascular control by novel methods of heart rate dynamics. Philos T R Soc A 2009; 367: 1223–1238.
  • 48. de Godoy MF, Takakura IT, Corrêa PR, Machado MN, Miranda RC, Brandi AC. Preoperative nonlinear behavior in heart rate variability predicts morbidity and mortality after coronary artery bypass graft surgery. Med Sci Monitor 2009; 15: 117–122.
  • 49. Corrêa PR, Catai AM, Takakura IT, Machado MN, de Godoy MF. Heart rate variability and pulmonary infections after myocardial revascularization. Arq Bras Cardiol 2010; 95: 448– 456.
  • 50. Pivatelli FC, dos Santos MA, Fernandes GB, Gatti M, de Abreu LC, Valenti VE, Vanderlei LC, Ferreira C, Adami F, de Carvalho TD et al. Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients. Int Arch Med 2012; 5: 31.
  • 51. Guzzetti S, Signorini MG, Cogliati C, Mezzetti S, Porta A, Cerutti S, Malliani A. Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and hearttransplanted patients. Cardiovasc Res 1996; 31: 441–446.
  • 52. Yılmaz D, Güler NF. Correlation dimension analysis of Doppler signals in children with aortic valve disorder. J Med Syst 2010; 34: 931–939.
  • 53. Teulier M, Fiamma MN, Straus C, Similowski T. Acute bronchodilation increases ventilatory complexity during resting breathing in stable COPD: toward mathematical biomarkers of ventilatory function? Resp Physiol Neurobi 2013; 185: 477–480.
  • 54. Kılıç YA. Chaos and complexity in medicine. In: Yılmaz E, Fen MO, editors. Proceedings of the 1st National Workshop on Complex Dynamical Systems and Applications; 12–13 October 2012; Ankara, Turkey. p. 12.
  • 55. Bates JHT. Lung Mechanics: An Inverse Modeling Approach. 1st ed. New York, NY, USA: Cambridge University Press; 2009.
  • 56. Korürek M, Yıldız M, Yüksel A. Simulation of normal cardiovascular system and severe aortic stenosis using equivalent electronic model. Anadolu Kardiyol Der 2010; 10: 471–478.
  • 57. Tirnakli U, Tsallis C, Beck C. Closer look at time averages of the logistic map at the edge of chaos. Phys Rev E 2009; 79: 056209.
  • 58. Yalcin GC, Skarlatos Y, Akdeniz KG. q-Gaussian analysis of the electronic behavior in polymethylmetacrylate. Chaos Solitons Fract 2013; 57: 73–78.