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Nonlinear Analyses of Data in Cardiovascular Physiology and Epidemiology

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Handbook of Psychocardiology

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Abstract

The nonlinear dynamics of heart action are such as to generate and to support irregular nonrandom variations in the main output parameters of pulse and pressure, in response to external stimulation such as stressors (Pearson 1972; Gregson 2009; Herbert 1995; Mezentseva et al. 2002; Rao and Yeragani 2001; Shiferaw and Karma 2006). These dynamic complexities have serious implications for the analysis and treatment of hypertension, as the probabilities of misdiagnosis of state, dysfunction, and potential morbidity cannot with certainty be based on the linear or Gaussian statistics usually employed in epidemiological and related studies. A Bayesian analysis of decision probabilities is used to point up ambiguities in reported results. There is gradual recognition of this situation, but so far little established linkage between nonlinear dynamical modeling and clinical practice, except perhaps in some recent biomedical physics modeling.

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References

  • Baron, J. (1994). Thinking and deciding (2nd ed.). New York: Cambridge University Press.

    Google Scholar 

  • Bassingthwaighte, J. B., King, R. B., & Roger, A. S. (1989). Fractal nature of regional myocardial blood flow heterogeneity. Circulation Research, 65, 578–590.

    Article  PubMed Central  PubMed  Google Scholar 

  • Bellavere, F. (1995). Heart rate variability in patients with diabetes and other noncardiological diseases. In M. Malik & A. J. Camm (Eds.), Heart rate variability (pp. 507–516). Armonk: Futura.

    Google Scholar 

  • Bunde, A., Kropp, J., & Schellnhuber, H. J. (2002). The science of disasters: Climate disruptions, heart attacks and market crashes. Berlin: Springer.

    Book  Google Scholar 

  • Byrne, D. G., & Rosenman, R. H. (1990). Anxiety and the heart. Washington, DC: Hemisphere Press.

    Google Scholar 

  • Chang, H.-S., Staras, K., & Gilbey, M. P. (2000). Multiple oscillators provide metastability in rhythm generation. Journal of Neurosciences, 20, 5135–5143.

    Google Scholar 

  • Clariá, F., Vallverdú, M., Baronowski, R., Chojnowska, L., & Caminal, P. (2008). Heart rate variability analysis based on time-frequency representation and entropies in hypertrophic cardiomyopathy patients. Physiological Measurement, 29(3), 401–416.

    Article  PubMed  Google Scholar 

  • Ditto, W. L. (1996). Applications of chaos in biology and medicine. In D. E. Herbert (Ed.), Chaos and the changing nature of science and medicine: An introduction (pp. 175–199). Woodbury: American Institute of Physics.

    Google Scholar 

  • Ebeling, W., Molgedey, L., Kurths, J., & Schwarz, U. (2002). Entropy, complexity, predictability and data analysis of time series and letter sequences. In A. Bunde, J. Kropp, & H. J. Schellnhuber (Eds.), The science of disasters: Climate disruptions, heart attacks and market crashes (pp. 1–25). Berlin: Springer.

    Google Scholar 

  • Ely, D. L. (1995). Organization of cardiovascular and neurohormonal responses to stress. In: Ely D. L. (Ed.) Stress: Basic mechanism and clinical implications. Annals of the New York Academy of Sciences, vol. 771 (pp. 594–608). New York: New York Academy of Sciences.

    Google Scholar 

  • Goldberger, A. L. (1990). Fractal electrodynamics of the heartbeat. In J. Jalife (Ed.), Mathematical approaches to cardiac arrhythmias (Annals of the New York Academy of Sciences, Vol. 591, pp. 402–409). New York: New York Academy of Sciences.

    Google Scholar 

  • Gregson, R. A. M. (1995). Cascades and fields in perceptual psychophysics. Singapore: World Scientific.

    Book  Google Scholar 

  • Gregson, R. A. M. (2002). Scaling quasi-periodic psychological functions. Behaviormetrika, 29, 41–57.

    Article  Google Scholar 

  • Gregson, R. A. M. (2005). Identifying ill-behaved nonlinear processes without metrics: The use of symbolic dynamics. Nonlinear Dynamics, Psychology, and Life Sciences, 9, 479–503.

    PubMed  Google Scholar 

  • Gregson, R. A. M. (2009). Conceptual problems in cardiological prediction. Nonlinear Dynamics, Psychology, and Life Sciences, 13, 207–222.

    Google Scholar 

  • Gregson, R. A. M. (2011). Frontiers of nonlinear methods. In S. J. Guastello & R. A. M. Gregson (Eds.), Nonlinear dynamical systems analysis for the behavioral sciences using real data (pp. 583–599). Clermont: Taylor and Francis. Chapter 25.

    Google Scholar 

  • Gregson, R. A. M., & Leahan, K. (2003). Forcing function effects on nonlinear trajectories: Identifying very local brain dynamics. Nonlinear Dynamics, Psychology, and Life Sciences, 7, 139–159.

    Article  PubMed  Google Scholar 

  • Gregson, R. A. M., & Pressing, J. L. (2000). Dynamic modelling. In J. T. Cacioppo, L. G. Tassinary, & G. G. Berntson (Eds.), Handbook of psychophysiology (2nd ed., pp. 924–948). New York: Cambridge University Press.

    Google Scholar 

  • Guidelines Committee of the ESH/ESC. (2003). European society of hypertension – European society of cardiology guidelines for the management of arterial hypertension. Journal of Hypertension, 21, 1011–1053.

    Article  Google Scholar 

  • Guzzetti, S., Signorini, M. G., Cogliati, C., Mezzetti, S., Porta, A., Cerutti, S., & Maliiani, A. (1996). Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart-transplanted patients. Cardiovascular Research, 31, 441–446.

    Article  PubMed  Google Scholar 

  • Herbert, D. (Ed.). (1995). Chaos and the changing nature of science and medicine, an introduction (Conference proceedings, 376). Woodbury: American Institute of Physics.

    Google Scholar 

  • Iverson, G. L., Stampfer, H. G. & Gaetz, M. (2000). Reliability of circadian heart pattern analysis in psychiatry. Paper presented at the annual conference of the Canadian Psychiatric Association, Victoria, BC. October 4, 2000.

    Google Scholar 

  • Klonowski, W. (2007). From conformons to human brains: An informal overview of nonlinear dynamics and its applications in biomedicine. Nonlinear Biomedical Physics, 1, 5. doi:10.1186/1753-4631-1-5.

    Article  PubMed Central  PubMed  Google Scholar 

  • Krypotos, A.-M., Jahfari, S., van Ast, V. A., Kindt, M., & Forstmann, B. U. (2011). Individual differences in heart rate variability predict the degree of slowing during response inhibition and initiation in the presence of emotional stimuli. Frontiers in Cognition. doi:10.3389, fpsyg.2011.00287.

    Google Scholar 

  • Laguzzi, R., Reis, D. J., & Talman, W. T. (1984). Modulation of cardiovascular and electrocortical activity through serotonergic mechanisms in the nucleus tractus solitarius of the rat. Brain Research, 304, 321–328.

    Article  PubMed  Google Scholar 

  • Ledford, A. W., & Tawn, J. A. (2003). Diagnostics for dependence within time series extremes. Journal of the Royal Statistical Society, Series B, 65, 521–543.

    Article  Google Scholar 

  • Malik, M., & Camm, A. J. (1995). Heart rate variability. Armonk: Fu-tura.

    Google Scholar 

  • Malliani, A., Pagani, M., Lombardi, F., & Cerutti, S. (1991). Cardiovascular neural regulation explored in the frequency domain. Circulation, 84, 482–492.

    Article  PubMed  Google Scholar 

  • Mezentseva, L. V., Kashtanov, S. I., Vostrikov, V. A., Zvyagintsev, M. A., & Kosharskaya, I. L. (2002). Chaos theory analysis of electrocardiograms recorded from humans and animals with ventricular fibrillation. Biophysics, 47, 352–358.

    Google Scholar 

  • Murray, J. D. (2002). Mathematical biology (Chapter 9: Perturbed and Coupled Oscillators and Black Holes 3rd ed.). New York: Springer.

    Google Scholar 

  • Nadis, S. (2003). All together now. Nature, 421, 780–782.

    Article  PubMed  Google Scholar 

  • National Institute of Occupational Health and Safety. (1987). Blood pressure study: Handbook of tables. Canberra: Australian Government Publishing Service.

    Google Scholar 

  • Niaura, R. (2002). Hostility and prediction of heart disease. Health Psychology, 21, 588–593.

    Google Scholar 

  • Parati, G., di Rienzo, M., & Mancia, G. (2001). Dynamic modulation of baroreflex sensitivity in health and disease. In M. W. Chapleau & F. M. Abboud (Eds.), Neuro-cardiovascular regulation: From molecules to Man (Annals of the New York Academy of Sciences, Vol. 940, pp. 469–487). New York: New York Academy of Sciences.

    Google Scholar 

  • Patel, C. (1990). Psychological and behavioral treatment of hypertension. In D. G. Byrne & R. H. Rosenman (Eds.), Anxiety and the heart (pp. 441–469). Washington: Hemisphere Press.

    Google Scholar 

  • Patel, C., Marmot, M. G., Terry, D. J., Carruthers, M., Hunt, & Patel, M. (1985). Trial of relaxation in reducing coronary risk: Four-year follow-up. British Medical Journal, 282, 2005–2008.

    Article  Google Scholar 

  • Pavićević, Ž., & Å uÅ¡ić, E. (2002). Application of the cyclic properties of dynamical systems to the study of the boundary limits of arbitrary functions. Doklady Mathematics, 66, 313–315.

    Google Scholar 

  • Pearson, E. S. and Hartley, H. O. (Eds.) (1972). Biometrika Tables for Statisticians, Vol. 1. Cambridge: Cambridge University Press.

    Google Scholar 

  • Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proceedings of the National Academy of Sciences of the USA, 88, 2297–2301.

    Article  PubMed Central  PubMed  Google Scholar 

  • Pincus, S. M. (2000). Approximate entropy in cardiology. Herzschliche Elek-trophysiologie, 11, 139–150.

    Article  Google Scholar 

  • Plamen, C. I., Goldberger, A. L., & Stanley, H. E. (2002). Fractal and multi-fractal approaches in physiology. In A. Bunde, J. Kropp, & H. J. Schellnhuber (Eds.), The science of disasters: Climate disruptions, heart attacks and market crashes (pp. 219–257). Berlin: Springer.

    Google Scholar 

  • Pollard, T. M., & Schwartz, J. E. (2003). Are changes in blood pressure and total cholesterol related to changes in mood? An 18-month study of men and women. Health Psychology, 22, 47–53.

    Article  PubMed  Google Scholar 

  • Porta, A., Furlan, R., Rimoldi, Pagani, M., Malliani, A., & van de Borne, P. (2002). Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals. Biological Cybernetics, 86, 241–251.

    Article  PubMed  Google Scholar 

  • Preitag, M. H., & Vasan, R. S. (2003). What is normal blood pressure? Current Opinions in Nephrology and Hypertension, 12, 285–292.

    Article  Google Scholar 

  • Rao, R. K. A., & Yeragani, V. K. (2001). Decreased chaos and increased non-linearity of heart rate time series in patients with panic disorder. Autonomic Neuroscience: Basic and Clinical, 88, 99–108.

    Article  Google Scholar 

  • Sarkar, A., & Barat, P. (2008). Effect of meditation on scaling behavior and complexity of human heart rate variability. Fractals, 16(3), 199–208.

    Article  Google Scholar 

  • Shepherd, J. T. (1985). The heart as a sensory organ. Journal of the American College of Cardiology, 5(6), 83B–87B.

    Article  PubMed  Google Scholar 

  • Shiferaw, Y., & Karma, A. (2006). Turing instability mediated by voltage and calcium diffusion in paced cardiac cells. Proceedings of the National Academy of Sciences of the USA, 103, 5670–5675.

    Article  PubMed Central  PubMed  Google Scholar 

  • Skinner, J. E. (1985). Regulation of cardiac vulnerability by the cerebral defense system. Journal of the American College of Cardiology, 5(6), 88B–94B.

    Article  PubMed  Google Scholar 

  • Sleight, P., & Casadei, B. (1995). Relationships between heart rate, respiration and blood pressure variabilities. In M. H. Malik & A. J. Camm (Eds.), Heart rate variability (pp. 311–325). Armonk: Futura.

    Google Scholar 

  • Steeb, W.-H. (2002). The nonlinear workbook (Chapter 7: Controlling and Synchronization of Chaos 2nd ed.). Singapore: World Scientific.

    Book  Google Scholar 

  • Stolarz, K., Staessen, J. A., Kuznetsova, T., Tikhonoff, V., State, D., Babeanu, S., Casiglia, E., Fagard, R. H., Kawecka-Jaszcz, K., Nikitin, Y., & European Project on Genes in Hypertension (EPOGH) Investigators. (2003). Journal of Hypertension, 21, 525–535.

    Article  PubMed  Google Scholar 

  • Strandberg, T. E., & Pitkala, K. (2003). What is the most important component of blood pressure: Systolic, diastolic or pulse pressure? Current Opinion in Nephrology and Hypertension, 12, 293–297.

    Article  PubMed  Google Scholar 

  • Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: A piecewise linear modeling framework. Chaos, 20(045102), 1–13.

    Google Scholar 

  • van de Borne, P., Montano, N., Narkiewicz, K., Degaute, J. P., Oren, P., Pagani, M., & Somers, V. K. (1998). Sympathetic rhythmicity in cardiac transplant recipients. Circulation, 99, 1606–1610.

    Article  Google Scholar 

  • Voss, A., Kurths, J., Kleiner, H. J., Witt, A., Wessel, N., Saparin, P., Osterziel, K. J., Schurath, R., & Dietz, R. (1996). The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovascular Research, 31, 419–433.

    Article  PubMed  Google Scholar 

  • Wang, S. Y., Zhang, L. F., Wang, X. B., & Cheng, J. H. (2000). Age dependency and correlation of heart rate variability, blood pressure variability and baroreflex sensitivity. Journal of Gravitational Physiology, 7, 145–146.

    Google Scholar 

  • Wessel, N., Voss, A., Malberg, H., Ziehmann, C., Voss, H. U., Schirdewan, A., Meyerfeldt, U., & Kurths, J. (2000). Nonlinear analysis of complex phenomena in cardiological data. Herzschrittmachertherapie und Elektrophysiologie, 11(3), 159–173.

    Article  Google Scholar 

  • Williams, S. P. (1998). The serotonin transporter: A primary target for antidepressant drugs. Journal of Psychopharmacology, 12(2), 15–121.

    Google Scholar 

  • Winfree, A. T. (1987). When time breaks down. Princeton: Princeton University Press.

    Google Scholar 

  • Wing, L. M. H., Reid, C. M., & Ryan, P. (2003). A comparison of outcome with angiotensin-converting-enzyme inhibitors and diuretics for hypertension in the elderly. New England Journal of Medicine, 348, 583–592.

    Article  PubMed  Google Scholar 

  • Wong, J., & Wolf, H. K. (2003). Secular trends and senescence of blood pressure in a Japanese and Yugoslavian cohort of the seven countries study. Blood Pressure, 12, 32–39.

    Article  PubMed  Google Scholar 

  • Yeragani, V. K., Krishna Rao, K. A. R., Smitha, M. R., Pohl, R. B., Balon, R., & Srinivasan, K. (2002). Diminished chaos of heart rate time series in patients with major depression. Biological Psychiatry, 51, 733–744.

    Article  PubMed  Google Scholar 

  • Zyczkowska, J., Klich-Raczka, A., Wizner, B., et al. (2003). Hypertension and cognitive impairment in centenarians. Journal of Hypertension, 21, S18. abstract 3B.3.

    Google Scholar 

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Authors and Affiliations

  1. Research School of Psychology, Australian National University, 0200, Canberra, ACT, Australia

    Robert A. M. Gregson

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  1. Robert A. M. Gregson
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Correspondence to Robert A. M. Gregson .

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Editors and Affiliations

  1. Monash University, Victoria, Australia

    Marlies Alvarenga

  2. Australia National University, Canberra, Aust Capital Terr, Australia

    Don Byrne

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Notes

I am indebted to Prof. Don Byrne for drawing my attention to a diversity of valuable sources on anxiety and heart function, including his own work. The mathematical interpretations are mostly my own.

The seventh report of the Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure (JNC7, May 2003, in the USA) introduced the notion of prehypertension. If this condition is defined by a single threshold value for SAP (120–139 mmHg is suggested), then logically, given the nonlinear variability of cardiac function, virtually all persons over a cutoff age of around 50 years will be at some times prehypertensive, and for them medical intervention is commended, including the reduced use of sodium in diet and at least to advise on lifestyle. It has been noted (www.medscape.com) that most of the authors of the report have extensive financial disclosures with numerous pharmaceutical companies. It must be emphasized that the recommendations of JNC7 have been strongly criticized, based in part on findings from the Second Australian National Blood Pressure Study (Wing et al. 2003). Some medical specialists, not starting from a base of nonlinear cardiac dynamics, but considering high plasma renin levels, have ridiculed the very existence of prehypertension.

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Gregson, R.A.M. (2015). Nonlinear Analyses of Data in Cardiovascular Physiology and Epidemiology. In: Alvarenga, M., Byrne, D. (eds) Handbook of Psychocardiology. Springer, Singapore. https://doi.org/10.1007/978-981-4560-53-5_46-1

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  • DOI: https://doi.org/10.1007/978-981-4560-53-5_46-1

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