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The biotic pattern of heartbeat intervals
Letters to the Editor
303
The biotic pattern of heartbeat intervals H. Sabelli a,⁎, J. Messer b, L. Kovacevic a, K. Walthall b a b
Chicago Center for Creative Development, 2400 N. Lakeview, Chicago, Illinois 60614, United States Rush University Medical Center, Chicago, Illinois, United States
a r t i c l e
i n f o
Article history: Received 25 September 2009 Accepted 17 October 2009 Keywords: Bios Creativity Cardiac failure
Heart rate variation (HRV) has become an important measure in the field of cardiology [1] but there still is limited understanding of how variation occurs and the reasons why low HRV has a negative prognostic value [2]. Empirical analysis demonstrates chaotic features [3,4] but rules out low-dimensional chaos and suggests stochastic processes [5]. A number of new techniques [6–8] detect features of creative processes in time series: (1) temporal complexity, multiple, time-limited patterns (complexes) in recurrence plots, (2) diversification, the increase in S.D. with increasingly larger samples (global diversification) or increasing embedding (local diversification); and (3) novelty, an increase in recurrence isometry by shuffling the data. The program used for these computations is available [9]. Temporal complexity, diversification, low isometry, and novelty are defining characteristics of Bios, a non-stationary, chaotic, and fractal pattern which is more sensitive to initial conditions than chaotic attractors. Bios differs from random walk in being generated causally, as demonstrated by temporal pattern in the series of differences between consecutive terms. Diversification, novelty, and temporal complexity are absent in series converging to an attractor. First identified in RR interval (RRI) series [10,11], Bios has been shown to be widespread in physical and human processes at all levels of organization: prime numbers [12], quantum wave functions [13,14]; temporal distribution of galaxies and of quasars [13,14]; gravitational waves [14,15], geographical structures [8], meteorological processes [8,14], animal populations [16], and economic processes [8]. We examined the long-term electrocardiographic recordings of RRI series of 54 subjects in normal sinus rhythm and 730 patients with cardiac failure of both sexes between 28 and 75 years old, obtained from the Physiobank database at (www.physionet.org/physiobank/ database), and compared the results with those obtained with models for the variations in heart rate: spare random numbers, random walks (generated by the successive addition of random numbers), chaos generated by the logistic equation A(t + 1) = g ⁎ A(t) ⁎ [1 − A(t)], and Bios generated by the process equation A(t + 1) = A(t) + g ⁎ sin(A(t) [17]. The pattern of RRI series closely approximates that of Bios in both healthy and cardiac failure patients. Recurrence plots reveal complex patterns that continuously vary in time [Fig. 1], closely resembling Bios generated through the process equation; chaotic and random series generate uniform plots. RRI series also show diversification, low
⁎ Corresponding author: Tel.: +1 773 348 5679. E-mail address: [email protected] (H. Sabelli).
recurrence isometry, and increase recurrence with shuffling the data, i.e. novelty. The series of differences between consecutive RRI shows high recurrence and a decrease in their numbers with shuffling, as in chaotic attractors, while differencing random walks generates random series. In short, HRV shows causation and the three distinctive features of creativity (diversification, novelty, and complexes varying in time), rather than maintenance of pattern. Heart failure significantly decreased isometry while conserving novelty, and slowed down diversification [Fig. 1]. These measurements may be useful for diagnosis as well as for the evaluation of therapeutic interventions. The significance of this study, however, does not reside in adding new methods for HRV analysis, but in highlighting the process that produces variation as being non-stationary, creative (not equilibrium or chaos), and causal (not stochastically generated by the coexistence of multiple factors). These results are thus significant regarding health. While Claude Bernard and Cannon stressed the importance of equilibrium, the studies of Goldberger and others highlighted the role of change and non-stationarity as essential to health. Bios fits this concept. We are thankful to the Society for the Advancement of Clinical Philosophy and to Mrs. Maria McCormick for her support. The authors certify that they comply with the Principles of Ethical Publishing in the International Journal of Cardiology [18]. References [1] Malik M, Camm AJ. Heart rate variability. Futura Publishing: Armonk; 1995. [2] Goldberger A, Challapalli S, Tung R, Parker M, Kadish AH. Relationship of heart rate variability to parasympathetic effect. Circulation 2001;103:1977–83. [3] Glass L, Mackey C. From clocks to chaos: the rhythms of life. Princeton University Press: Princeton; 1988. [4] Wessel N, Kurths J, Malberg H, Bauernschmitt R. Introduction: cardiovascular physics. Chaos 2007;17:15–101. [5] Cecen A, Erkal C. The Long March: from monofractals to endogenous multifractality in heart rate variability analysis. Nonlinear Dyn Psychol Life 2009;13 (2):181–206. [6] Sabelli H, Abouzeid A. Definition and empirical characterization of creative processes. Nonlinear Dyn Psychol Life 2003;7:35–47. [7] Sabelli H. Novelty, a measure of creative organization in natural and mathematical time series. Nonlinear Dyn Psychol Life 2001;5:89–113. [8] Sabelli H. Bios. A study of creation. Singapore: World Scientific; 2005. [9] http://www.inverudio.com/programs/BiosAnalyzer/BiosAnalyzer.php. [10] Carlson-Sabelli L, Sabelli HC, Zbilut J, Patel M, Messer J, Walthall K, Tom C, Fink P, Sugerman A, Zdanovics O. How the heart informs about the brain. A process analysis of the electrocardiogram. In: Trappl R, editor. Cybernetics and systems, 2. Singapore: World Scientific; 1994. p. 1031–8. [11] Sabelli HC, Carlson-Sabelli L, Patel M, Zbilut J, Messer J, Walthall K. Psychocardiological portraits: a clinical application of process theory. In: Abraham FD, Gilgen AR, editors. Chaos theory in psychology. Westport, CT: Greenwood Publishing Group, Inc; 1995. p. 107–25. [12] Sabelli H. The Biotic Pattern of Prime Numbers. Cybernetics and Systemics Journal (in press). [13] Sabelli H, Kovacevic L. Quantum Bios and biotic complexity in the distribution of galaxies. Complexity 2006;11:14–25. [14] Sabelli H, Thomas J, Kovacevic L, Lawandow A, Horan D. Biotic dynamics of galactic distribution, gravitational waves, and quantum processes. A causal theory of cosmological evolution. In Wachter AD, Propst RJ (Eds.) Black Holes and Galaxy Formation. Nova Science Publishers, in press. [15] Sabelli H, Lawandow A. Complex biotic patterns in the recordings from LIGO. Complexity, in press. [16] Sabelli H, Kovacevic. Biotic complexity of population dynamics. Complexity 2008;13(4):47–55. [17] Kauffman L, Sabelli H. The process equation. Cybern Syst 1998;29(4):345–62. [18] Coats AJ. Ethical authorship and publishing. Int J Cardiol 2009;131:149–50.
304
Letters to the Editor
Fig. 1. Top: Recurrence plots (50 embeddings, 10% cutoff radius, 100,000 comparisons). Top left: RRI from healthy subject. Top right: Series of differences. Bottom: Average and S.D. of net isometry (data minus shuffled copy) and of S.D. at 1, 2,… 30 embeddings.
0167-5273/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ijcard.2009.10.040
303
The biotic pattern of heartbeat intervals H. Sabelli a,⁎, J. Messer b, L. Kovacevic a, K. Walthall b a b
Chicago Center for Creative Development, 2400 N. Lakeview, Chicago, Illinois 60614, United States Rush University Medical Center, Chicago, Illinois, United States
a r t i c l e
i n f o
Article history: Received 25 September 2009 Accepted 17 October 2009 Keywords: Bios Creativity Cardiac failure
Heart rate variation (HRV) has become an important measure in the field of cardiology [1] but there still is limited understanding of how variation occurs and the reasons why low HRV has a negative prognostic value [2]. Empirical analysis demonstrates chaotic features [3,4] but rules out low-dimensional chaos and suggests stochastic processes [5]. A number of new techniques [6–8] detect features of creative processes in time series: (1) temporal complexity, multiple, time-limited patterns (complexes) in recurrence plots, (2) diversification, the increase in S.D. with increasingly larger samples (global diversification) or increasing embedding (local diversification); and (3) novelty, an increase in recurrence isometry by shuffling the data. The program used for these computations is available [9]. Temporal complexity, diversification, low isometry, and novelty are defining characteristics of Bios, a non-stationary, chaotic, and fractal pattern which is more sensitive to initial conditions than chaotic attractors. Bios differs from random walk in being generated causally, as demonstrated by temporal pattern in the series of differences between consecutive terms. Diversification, novelty, and temporal complexity are absent in series converging to an attractor. First identified in RR interval (RRI) series [10,11], Bios has been shown to be widespread in physical and human processes at all levels of organization: prime numbers [12], quantum wave functions [13,14]; temporal distribution of galaxies and of quasars [13,14]; gravitational waves [14,15], geographical structures [8], meteorological processes [8,14], animal populations [16], and economic processes [8]. We examined the long-term electrocardiographic recordings of RRI series of 54 subjects in normal sinus rhythm and 730 patients with cardiac failure of both sexes between 28 and 75 years old, obtained from the Physiobank database at (www.physionet.org/physiobank/ database), and compared the results with those obtained with models for the variations in heart rate: spare random numbers, random walks (generated by the successive addition of random numbers), chaos generated by the logistic equation A(t + 1) = g ⁎ A(t) ⁎ [1 − A(t)], and Bios generated by the process equation A(t + 1) = A(t) + g ⁎ sin(A(t) [17]. The pattern of RRI series closely approximates that of Bios in both healthy and cardiac failure patients. Recurrence plots reveal complex patterns that continuously vary in time [Fig. 1], closely resembling Bios generated through the process equation; chaotic and random series generate uniform plots. RRI series also show diversification, low
⁎ Corresponding author: Tel.: +1 773 348 5679. E-mail address: [email protected] (H. Sabelli).
recurrence isometry, and increase recurrence with shuffling the data, i.e. novelty. The series of differences between consecutive RRI shows high recurrence and a decrease in their numbers with shuffling, as in chaotic attractors, while differencing random walks generates random series. In short, HRV shows causation and the three distinctive features of creativity (diversification, novelty, and complexes varying in time), rather than maintenance of pattern. Heart failure significantly decreased isometry while conserving novelty, and slowed down diversification [Fig. 1]. These measurements may be useful for diagnosis as well as for the evaluation of therapeutic interventions. The significance of this study, however, does not reside in adding new methods for HRV analysis, but in highlighting the process that produces variation as being non-stationary, creative (not equilibrium or chaos), and causal (not stochastically generated by the coexistence of multiple factors). These results are thus significant regarding health. While Claude Bernard and Cannon stressed the importance of equilibrium, the studies of Goldberger and others highlighted the role of change and non-stationarity as essential to health. Bios fits this concept. We are thankful to the Society for the Advancement of Clinical Philosophy and to Mrs. Maria McCormick for her support. The authors certify that they comply with the Principles of Ethical Publishing in the International Journal of Cardiology [18]. References [1] Malik M, Camm AJ. Heart rate variability. Futura Publishing: Armonk; 1995. [2] Goldberger A, Challapalli S, Tung R, Parker M, Kadish AH. Relationship of heart rate variability to parasympathetic effect. Circulation 2001;103:1977–83. [3] Glass L, Mackey C. From clocks to chaos: the rhythms of life. Princeton University Press: Princeton; 1988. [4] Wessel N, Kurths J, Malberg H, Bauernschmitt R. Introduction: cardiovascular physics. Chaos 2007;17:15–101. [5] Cecen A, Erkal C. The Long March: from monofractals to endogenous multifractality in heart rate variability analysis. Nonlinear Dyn Psychol Life 2009;13 (2):181–206. [6] Sabelli H, Abouzeid A. Definition and empirical characterization of creative processes. Nonlinear Dyn Psychol Life 2003;7:35–47. [7] Sabelli H. Novelty, a measure of creative organization in natural and mathematical time series. Nonlinear Dyn Psychol Life 2001;5:89–113. [8] Sabelli H. Bios. A study of creation. Singapore: World Scientific; 2005. [9] http://www.inverudio.com/programs/BiosAnalyzer/BiosAnalyzer.php. [10] Carlson-Sabelli L, Sabelli HC, Zbilut J, Patel M, Messer J, Walthall K, Tom C, Fink P, Sugerman A, Zdanovics O. How the heart informs about the brain. A process analysis of the electrocardiogram. In: Trappl R, editor. Cybernetics and systems, 2. Singapore: World Scientific; 1994. p. 1031–8. [11] Sabelli HC, Carlson-Sabelli L, Patel M, Zbilut J, Messer J, Walthall K. Psychocardiological portraits: a clinical application of process theory. In: Abraham FD, Gilgen AR, editors. Chaos theory in psychology. Westport, CT: Greenwood Publishing Group, Inc; 1995. p. 107–25. [12] Sabelli H. The Biotic Pattern of Prime Numbers. Cybernetics and Systemics Journal (in press). [13] Sabelli H, Kovacevic L. Quantum Bios and biotic complexity in the distribution of galaxies. Complexity 2006;11:14–25. [14] Sabelli H, Thomas J, Kovacevic L, Lawandow A, Horan D. Biotic dynamics of galactic distribution, gravitational waves, and quantum processes. A causal theory of cosmological evolution. In Wachter AD, Propst RJ (Eds.) Black Holes and Galaxy Formation. Nova Science Publishers, in press. [15] Sabelli H, Lawandow A. Complex biotic patterns in the recordings from LIGO. Complexity, in press. [16] Sabelli H, Kovacevic. Biotic complexity of population dynamics. Complexity 2008;13(4):47–55. [17] Kauffman L, Sabelli H. The process equation. Cybern Syst 1998;29(4):345–62. [18] Coats AJ. Ethical authorship and publishing. Int J Cardiol 2009;131:149–50.
304
Letters to the Editor
Fig. 1. Top: Recurrence plots (50 embeddings, 10% cutoff radius, 100,000 comparisons). Top left: RRI from healthy subject. Top right: Series of differences. Bottom: Average and S.D. of net isometry (data minus shuffled copy) and of S.D. at 1, 2,… 30 embeddings.
0167-5273/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ijcard.2009.10.040