Nonlinear Analysis of Physiological Time Series

Biological systems and processes are inherently complex, nonlinear and nonstationary, and that is why nonlinear time series analysis has emerged as a novel methodology over the past few decades. The aim of this chapter is to provide a review of main approaches of nonlinear analysis (fractal analysis, chaos theory, complexity measures) in physiological research, from system modeling to methodological analysis and clinical applications.

[1]  Jeffrey M. Hausdorff,et al.  Physionet: Components of a New Research Resource for Complex Physiologic Signals". Circu-lation Vol , 2000 .

[2]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[3]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[4]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[5]  K Lehnertz,et al.  Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy--an overview. , 1999, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[6]  H. Huikuri,et al.  Altered complexity and correlation properties of R-R interval dynamics before the spontaneous onset of paroxysmal atrial fibrillation. , 1999, Circulation.

[7]  K. Newell,et al.  Changing complexity in human behavior and physiology through aging and disease , 2002, Neurobiology of Aging.

[8]  Henry D. I. Abarbanel,et al.  Variation of Lyapunov exponents on a strange attractor , 1991 .

[9]  C. Stam,et al.  Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field , 2005, Clinical Neurophysiology.

[10]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[11]  D. T. Kaplan,et al.  Nonlinearity and nonstationarity: the use of surrogate data in interpreting fluctuations , 1997 .

[12]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[13]  Jeffrey M. Hausdorff,et al.  Quantifying Fractal Dynamics of Human Respiration: Age and Gender Effects , 2002, Annals of Biomedical Engineering.

[14]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[15]  Harvard Medical School,et al.  Effect of nonstationarities on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  H. Preissl,et al.  Detrended fluctuation analysis of short datasets : An application to fetal cardiac data , 2007 .

[17]  M. J. Katz,et al.  Fractals and the analysis of waveforms. , 1988, Computers in biology and medicine.

[18]  Jianqing Fan.  Nonlinear Time Series , 2003 .

[19]  Thomas Schreiber,et al.  IS NONLINEARITY EVIDENT IN TIME SERIES OF BRAIN ELECTRICAL ACTIVITY , 2000 .

[20]  T Seppänen,et al.  Power-law relationship of heart rate variability as a predictor of mortality in the elderly. , 1998, Circulation.

[21]  J. J. Collins,et al.  Age-related changes in open-loop and closed-loop postural control mechanisms , 2004, Experimental Brain Research.

[22]  Arthur Petrosian,et al.  Kolmogorov complexity of finite sequences and recognition of different preictal EEG patterns , 1995, Proceedings Eighth IEEE Symposium on Computer-Based Medical Systems.

[23]  Ong Wai Sing,et al.  Heart rate analysis in normal subjects of various age groups , 2004, Biomedical engineering online.

[24]  María Eugenia Torres,et al.  Automatic Detection of Slight Changes in nonlinear Dynamical Systems using Multiresolution Entropy Tools , 2001, Int. J. Bifurc. Chaos.

[25]  A L Goldberger,et al.  Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction. , 2000, Circulation.

[26]  Andrea Caumo,et al.  Approximate entropy of respiratory patterns in panic disorder. , 2004, The American journal of psychiatry.

[27]  F. Yates.  Order and complexity in dynamical systems: Homeodynamics as a generalized mechanics for biology , 1994 .

[28]  P. Grassberger,et al.  Estimation of the Kolmogorov entropy from a chaotic signal , 1983 .

[29]  Anne Beuter,et al.  Nonlinear dynamics in physiology and medicine , 2003 .

[30]  J. Kwapień,et al.  Wavelet versus detrended fluctuation analysis of multifractal structures. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  A L Goldberger,et al.  Heart rate dynamics in patients with stable angina pectoris and utility of fractal and complexity measures. , 1998, The American journal of cardiology.

[33]  Schreiber,et al.  Improved Surrogate Data for Nonlinearity Tests. , 1996, Physical review letters.

[34]  H. Stanley,et al.  Behavioral-independent features of complex heartbeat dynamics. , 2001, Physical review letters.

[35]  A. Goldberger.  Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside , 1996, The Lancet.

[36]  J. Dingwell,et al.  Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. , 2006, Journal of biomechanics.

[37]  P. Grassberger,et al.  NONLINEAR TIME SEQUENCE ANALYSIS , 1991 .

[38]  M. Teich,et al.  Fractal-Based Point Processes , 2005 .

[39]  Jeffrey M. Hausdorff,et al.  Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. , 1996, Journal of applied physiology.

[40]  L. Lipsitz.  Dynamics of stability: the physiologic basis of functional health and frailty. , 2002, The journals of gerontology. Series A, Biological sciences and medical sciences.

[41]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[42]  H E Stanley,et al.  Statistical physics and physiology: monofractal and multifractal approaches. , 1999, Physica A.

[43]  Jeffrey M. Hausdorff,et al.  Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. , 1995, Journal of applied physiology.

[44]  R. Newton,et al.  Discriminating between elderly and young using a fractal dimension analysis of centre of pressure , 2004, International journal of medical sciences.

[45]  J. Dingwell,et al.  Nonlinear time series analysis of normal and pathological human walking. , 2000, Chaos.

[46]  Pere Caminal,et al.  Detrended Fluctuation Analysis of EEG as a Measure of Depth of Anesthesia , 2007, IEEE Transactions on Biomedical Engineering.

[47]  Shaun Lovejoy,et al.  THE MULTIFRACTAL SCALING OF CLOUD RADIANCES FROM 1M TO 1KM , 2002 .

[48]  H. Huikuri,et al.  Fractal analysis and time- and frequency-domain measures of heart rate variability as predictors of mortality in patients with heart failure. , 2001, The American journal of cardiology.

[49]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[50]  G. Bleijenberg,et al.  Decreased Fractal Correlation in Diurnal Physical Activity in Chronic Fatigue Syndrome , 2004, Methods of Information in Medicine.

[51]  Robert G. Turcott,et al.  Fractal character of the electrocardiogram: Distinguishing heart-failure and normal patients , 1996, Annals of Biomedical Engineering.

[52]  M Tulppo,et al.  Abnormalities in beat to beat complexity of heart rate dynamics in patients with a previous myocardial infarction. , 1996, Journal of the American College of Cardiology.

[53]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[54]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[55]  Vladimir M. Zatsiorsky,et al.  On the fractal properties of natural human standing , 2000, Neuroscience Letters.

[56]  Teodor Buchner,et al.  Symbolic dynamics and complexity in a physiological time series , 2000 .

[57]  Toshiyo Tamura,et al.  Fractal dynamics of body motion in patients with Parkinson's disease , 2004, Journal of neural engineering.

[58]  Jeffrey M. Hausdorff,et al.  Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease. , 1997, Journal of applied physiology.

[59]  E. Martin,et al.  Kinematics and dynamic complexity of postural transitions in frail elderly subjects , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[60]  James Theiler,et al.  On the evidence for how-dimensional chaos in an epileptic electroencephalogram , 1995 .

[61]  A. Goldberger.  Fractal Variability Versus Pathologic Periodicity: Complexity Loss and Stereotypy in Disease , 1997, Perspectives in biology and medicine.

[62]  J. F. Brewster,et al.  Fractal ventilation enhances respiratory sinus arrhythmia , 2005, Respiratory research.

[63]  J. Collins,et al.  Random walking during quiet standing. , 1994, Physical review letters.

[64]  Roberto Hornero,et al.  Interpretation of the Lempel-Ziv Complexity Measure in the Context of Biomedical Signal Analysis , 2006, IEEE Transactions on Biomedical Engineering.

[65]  A L Goldberger,et al.  Dynamic analysis of heart rate may predict subsequent ventricular tachycardia after myocardial infarction. , 1997, The American journal of cardiology.

[66]  Ary L. Goldberger,et al.  Complex Systems , 2006, Intelligenza Artificiale.

[67]  D. Levy,et al.  Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics. , 1997, Circulation.

[68]  Karl M Newell,et al.  Complexity in aging and disease: response to commentaries , 2002, Neurobiology of Aging.

[69]  J. Havstad,et al.  Attractor dimension of nonstationary dynamical systems from small data sets. , 1989, Physical review. A, General physics.

[70]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[71]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[72]  K. Müller,et al.  Noise robust estimates of correlation dimension and K2 entropy. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[73]  A. Arneodo,et al.  Wavelet transform of multifractals. , 1988, Physical review letters.

[74]  Alan V. Sahakian,et al.  Use of Sample Entropy Approach to Study Heart Rate Variability in Obstructive Sleep Apnea Syndrome , 2007, IEEE Transactions on Biomedical Engineering.

[75]  T. Higuchi.  Approach to an irregular time series on the basis of the fractal theory , 1988 .

[76]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[77]  Shlomo Havlin,et al.  Multifractality of river runoff and precipitation: Comparison of fluctuation analysis and wavelet methods , 2003 .

[78]  M. Tancer,et al.  Nonlinear Measures of Respiration: Respiratory Irregularity and Increased Chaos of Respiration in Patients with Panic Disorder , 2002, Neuropsychobiology.

[79]  Peter Grassberger,et al.  Entropy estimation of symbol sequences. , 1996, Chaos.

[80]  M. Arif,et al.  Estimation of the Effect of Cadence on Gait Stability in Young and Elderly People using Approximate Entropy Technique , 2004 .

[81]  S. Havlin,et al.  Detecting long-range correlations with detrended fluctuation analysis , 2001, cond-mat/0102214.

[82]  Cornelis J. Stam,et al.  Nonlinear Brain Dynamics , 2006 .

[83]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[84]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[85]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[86]  K. Aminian,et al.  Nonlinear analysis of human physical activity patterns in health and disease. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[87]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[88]  M. Rosenstein,et al.  Reconstruction expansion as a geometry-based framework for choosing proper delay times , 1994 .

[89]  Brian Litt,et al.  A comparison of waveform fractal dimension algorithms , 2001 .

[90]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[91]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[92]  Steven B. Lowen,et al.  Fractal-Based Point Processes , 2005 .

[93]  P. Agostino Accardo,et al.  Use of the fractal dimension for the analysis of electroencephalographic time series , 1997, Biological Cybernetics.

[94]  Liacir S. Lucena,et al.  Power law temporal auto-correlations in day-long records of human physical activity and their alteration with disease , 2004 .

[95]  H. Abarbanel,et al.  Local false nearest neighbors and dynamical dimensions from observed chaotic data. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[96]  L. Glass,et al.  Understanding Nonlinear Dynamics , 1995 .

[97]  Malvin C. Teich,et al.  Fractal neuronal firing patterns , 1992 .

[98]  L. Lipsitz.  Physiological complexity, aging, and the path to frailty. , 2004, Science of aging knowledge environment : SAGE KE.

[99]  J. Richman,et al.  Physiological time-series analysis using approximate entropy and sample entropy. , 2000, American journal of physiology. Heart and circulatory physiology.

[100]  Robert G. Turcott,et al.  The Fractal Doubly Stochastic Poisson Point Process as a Model for the Cochlear Neural Spike Train , 1990 .

[101]  C. Peng,et al.  What is physiologic complexity and how does it change with aging and disease? , 2002, Neurobiology of Aging.

[102]  Madalena Costa,et al.  Multiscale entropy analysis of complex physiologic time series. , 2002, Physical review letters.

[103]  Richard E.A. van Emmerik,et al.  On the functional aspects of variability in postural control. , 2002 .

[104]  Mary Koithan,et al.  Models for the Study of Whole Systems , 2006, Integrative cancer therapies.

[105]  M Akay,et al.  Fractal dynamics of body motion in post-stroke hemiplegic patients during walking , 2004, Journal of neural engineering.

[106]  K Lehnertz,et al.  Nonlinear EEG Analysis and Its Potential Role in Epileptology , 2000, Epilepsia.

[107]  S. Leistedt,et al.  Characterization of the sleep EEG in acutely depressed men using detrended fluctuation analysis , 2007, Clinical Neurophysiology.

[108]  Carlos Sevcik,et al.  A procedure to Estimate the Fractal Dimension of Waveforms , 2010, 1003.5266.

[109]  P. Grassberger.  An optimized box-assisted algorithm for fractal dimensions , 1990 .

[110]  Hans G. Feichtinger,et al.  Analysis, Synthesis, and Estimation of Fractal-Rate Stochastic Point Processes , 1997, adap-org/9709006.

[111]  Andreas Galka,et al.  Topics in Nonlinear Time Series Analysis, with Implications for Eeg Analysis , 2000 .

[112]  Jeffrey M. Hausdorff,et al.  Dynamic markers of altered gait rhythm in amyotrophic lateral sclerosis. , 2000, Journal of applied physiology.

[113]  Teich,et al.  Doubly stochastic Poisson point process driven by fractal shot noise. , 1991, Physical Review A. Atomic, Molecular, and Optical Physics.

[114]  D. Cox,et al.  The statistical analysis of series of events , 1966 .

[115]  M. Teich,et al.  Fractal character of the neural spike train in the visual system of the cat. , 1997, Journal of the Optical Society of America. A, Optics, image science, and vision.