Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.

[1]  W. Zung.  A SELF-RATING DEPRESSION SCALE. , 1965, Archives of general psychiatry.

[2]  M. Hoehn,et al.  Parkinsonism , 1967, Neurology.

[3]  V. C. Conde López,et al.  [Zung's self-rating depression scale]. , 1969, Archivos de neurobiologia.

[4]  E. Braunwald,et al.  Survival of patients with severe congestive heart failure treated with oral milrinone. , 1986, Journal of the American College of Cardiology.

[5]  R. Tibshirani,et al.  Local Likelihood Estimation , 1987 .

[6]  W. Gibb,et al.  The relevance of the Lewy body to the pathogenesis of idiopathic Parkinson's disease. , 1988, Journal of neurology, neurosurgery, and psychiatry.

[7]  P Lemoine,et al.  Heart rate circadian rhythm as a biological marker of desynchronization in major depression: a methodological and preliminary report. , 1990, Chronobiology international.

[8]  Ulrich Parlitz,et al.  Comparison of Different Methods for Computing Lyapunov Exponents , 1990 .

[9]  U. Parlitz,et al.  Lyapunov exponents from time series , 1991 .

[10]  M. Korenberg,et al.  Orthogonal approaches to time-series analysis and system identification , 1991, IEEE Signal Processing Magazine.

[11]  P Lemoine,et al.  Sleep and heart rate circadian rhythm in depression: the necessity to separate. , 1993, Chronobiology international.

[12]  R. Kessler,et al.  Lifetime and 12-month prevalence of DSM-III-R psychiatric disorders in the United States. Results from the National Comorbidity Survey. , 1994, Archives of general psychiatry.

[13]  R. Hughson,et al.  On the fractal nature of heart rate variability in humans: effects of data length and beta-adrenergic blockade. , 1994, The American journal of physiology.

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

[15]  Shlomo Havlin,et al.  Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis , 1996, Nature.

[16]  Jørgen K. Kanters,et al.  Short- and long-term variations in non-linear dynamics of heart rate variability. , 1996, Cardiovascular research.

[17]  L. Forno,et al.  Neuropathology of Parkinson's Disease , 1996, Journal of neuropathology and experimental neurology.

[18]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[19]  R J Cohen,et al.  Detection of chaotic determinism in time series from randomly forced maps. , 1997, Physica D. Nonlinear phenomena.

[20]  O. Rascol,et al.  Prevalence of orthostatic hypotension in Parkinson’s disease , 1997, Journal of neurology, neurosurgery, and psychiatry.

[21]  R. Russell,et al.  On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems , 1997 .

[22]  H. Stampfer,et al.  The Relationship between Psychiatric Illness and the Circadian Pattern of Heart Rate , 1998, The Australian and New Zealand journal of psychiatry.

[23]  R. Prescott,et al.  Prospective study of heart rate variability and mortality in chronic heart failure: results of the United Kingdom heart failure evaluation and assessment of risk trial (UK-heart). , 1998, Circulation.

[24]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[25]  Ivanov PCh,et al.  Stochastic feedback and the regulation of biological rhythms , 1998 .

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

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

[28]  Amir B. Geva,et al.  Autonomic dysregulation in panic disorder and in post-traumatic stress disorder: application of power spectrum analysis of heart rate variability at rest and in response to recollection of trauma or panic attacks , 2000, Psychiatry Research.

[29]  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.

[30]  Metin Akay,et al.  Nonlinear Biomedical Signal Processing, Dynamic Analysis and Modeling , 2000 .

[31]  S. Havlin,et al.  Correlated and uncorrelated regions in heart-rate fluctuations during sleep. , 2000, Physical review letters.

[32]  S. Guzzetti,et al.  Physiological time-series analysis using approximate entropy and sample entropy , 2000 .

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

[34]  Metin Akay,et al.  Nonlinear Biomedical Signal Processing Vol. II: Dynamic Analysis and Modeling , 2000 .

[35]  J. Davidson,et al.  Clinician‐administered PTSD scale: A review of the first ten years of research , 2001, Depression and anxiety.

[36]  M. Hoehn,et al.  Parkinsonism , 1998, Neurology.

[37]  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.

[38]  Clive W. J. Granger,et al.  An introduction to long-memory time series models and fractional differencing , 2001 .

[39]  H. Huikuri,et al.  Ambulatory ECG and analysis of heart rate variability in Parkinson's disease , 2001, Journal of neurology, neurosurgery, and psychiatry.

[40]  R. Carney,et al.  Depression as a risk factor for cardiac mortality and morbidity: a review of potential mechanisms. , 2002, Journal of psychosomatic research.

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

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

[43]  Cavit Boz,et al.  Relationship between major depression and heart rate variability. Clinical consequences and implications for antidepressive treatment , 2002, Psychiatry Research.

[44]  The Unified Parkinson's Disease Rating Scale (UPDRS): Status and recommendations , 2003, Movement disorders : official journal of the Movement Disorder Society.

[45]  O. Stiedl,et al.  Fractal dynamics in circadian cardiac time series of corticotropin-releasing factor receptor subtype-2 deficient mice , 2003, Journal of mathematical biology.

[46]  Jeffrey M. Hausdorff,et al.  Heart rate dynamics during three forms of meditation. , 2004, International journal of cardiology.

[47]  Ki H. Chon,et al.  A Stochastic Nonlinear Autoregressive Algorithm Reflects Nonlinear Dynamics of Heart-Rate Fluctuations , 2002, Annals of Biomedical Engineering.

[48]  Karl M Newell,et al.  Age-related changes in complexity depend on task dynamics. , 2004, Journal of applied physiology.

[49]  Hansjürgen Bratzke,et al.  Stages in the development of Parkinson’s disease-related pathology , 2004, Cell and Tissue Research.

[50]  Stefan Braune,et al.  Symptoms of autonomic failure in Parkinson’s disease: prevalence and impact on daily life , 2005, Clinical Autonomic Research.

[51]  W. Hoefnagels,et al.  Autonomic dysfunction in Parkinson's disease, tested with a computerized method using a Finapres device , 1995, Clinical Autonomic Research.

[52]  Stefano Pini,et al.  Prevalence and burden of bipolar disorders in European countries , 2005, European Neuropsychopharmacology.

[53]  Edward J. Rzempoluck,et al.  A New Potential Marker for Abnormal Cardiac Physiology in Depression , 2005, Journal of Behavioral Medicine.

[54]  K. Sunagawa,et al.  Dynamic nonlinear vago-sympathetic interaction in regulating heart rate , 2005, Heart and Vessels.

[55]  E. Brown,et al.  A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability. , 2005, American journal of physiology. Heart and circulatory physiology.

[56]  Michael J. Korenberg,et al.  Parallel cascade identification and kernel estimation for nonlinear systems , 2006, Annals of Biomedical Engineering.

[57]  V. Marmarelis.  Identification of nonlinear biological systems using laguerre expansions of kernels , 1993, Annals of Biomedical Engineering.

[58]  A. M. Bianchi,et al.  Comparison of heart rate variability analysis methods in patients with Parkinson's disease , 2002, Medical and Biological Engineering and Computing.

[59]  U. Rajendra Acharya,et al.  Heart rate variability: a review , 2006, Medical and Biological Engineering and Computing.

[60]  Emery N. Brown,et al.  Analysis of heartbeat dynamics by point process adaptive filtering , 2006, IEEE Transactions on Biomedical Engineering.

[61]  C. Alessi,et al.  Practice parameters for the psychological and behavioral treatment of insomnia: an update. An american academy of sleep medicine report. , 2006, Sleep.

[62]  T. Morgenthaler,et al.  Complex sleep apnea syndrome: is it a unique clinical syndrome? , 2006, Sleep.

[63]  Daniel T. Schmitt,et al.  Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly. , 2007, American journal of physiology. Regulatory, integrative and comparative physiology.

[64]  Benicio N Frey,et al.  Oxidative stress markers in bipolar disorder: a meta-analysis. , 2008, Journal of affective disorders.

[65]  Emery N. Brown,et al.  Characterizing nonlinear heartbeat dynamics within a point process framework , 2010, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[66]  H. Braak,et al.  Invited Article: Nervous system pathology in sporadic Parkinson disease , 2008, Neurology.

[67]  L. Dierker,et al.  Does number of lifetime traumas explain the relationship between PTSD and chronic medical conditions? Answers from the National Comorbidity Survey-Replication (NCS-R) , 2008, Journal of Behavioral Medicine.

[68]  Junichiro Hayano,et al.  Non-Gaussian heart rate as an independent predictor of mortality in patients with chronic heart failure. , 2008, Heart rhythm.

[69]  Pere Caminal,et al.  Methods derived from nonlinear dynamics for analysing heart rate variability , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[70]  Plamen Ch. Ivanov,et al.  Stratification Pattern of Static and Scale-Invariant Dynamic Measures of Heartbeat Fluctuations Across Sleep Stages in Young and Elderly , 2009, IEEE Transactions on Biomedical Engineering.

[71]  Emery N. Brown,et al.  Assessment of Autonomic Control and Respiratory Sinus Arrhythmia Using Point Process Models of Human Heart Beat Dynamics , 2009, IEEE Transactions on Biomedical Engineering.

[72]  Sid Gilman,et al.  Prospective differentiation of multiple system atrophy from Parkinson disease, with and without autonomic failure. , 2009, Archives of neurology.

[73]  Leon Glass,et al.  Introduction to controversial topics in nonlinear science: is the normal heart rate chaotic? , 2009, Chaos.

[74]  H. Wagner,et al.  Sleep disturbance and baroreceptor sensitivity in women with posttraumatic stress disorder. , 2009, Journal of traumatic stress.

[75]  Natalia M. Arzeno,et al.  Chaotic Signatures of Heart Rate Variability and Its Power Spectrum in Health, Aging and Heart Failure , 2009, PloS one.

[76]  K. Bär,et al.  The altered complexity of cardiovascular regulation in depressed patients , 2010, Physiological measurement.

[77]  Eduard Vieta,et al.  Staging Bipolar Disorder , 2011, Neurotoxicity Research.

[78]  Emery N. Brown,et al.  Dynamic Assessment of Baroreflex Control of Heart Rate During Induction of Propofol Anesthesia Using a Point Process Method , 2010, Annals of Biomedical Engineering.

[79]  Peter J. Schwartz,et al.  Sympathetic–parasympathetic interaction in health and disease: abnormalities and relevance in heart failure , 2011, Heart Failure Reviews.

[80]  Riccardo Barbieri,et al.  Characterizing Nonlinear Heartbeat Dynamics Within a Point Process Framework , 2008, IEEE Transactions on Biomedical Engineering.

[81]  Joachim M. Buhmann,et al.  The Balanced Accuracy and Its Posterior Distribution , 2010, 2010 20th International Conference on Pattern Recognition.

[82]  Zbigniew R. Struzik,et al.  Increased Non-Gaussianity of Heart Rate Variability Predicts Cardiac Mortality after an Acute Myocardial Infarction , 2011, Front. Physio..

[83]  E. Walker,et al.  Diagnostic and Statistical Manual of Mental Disorders , 2013 .

[84]  A L Goldberger,et al.  Decreased neuroautonomic complexity in men during an acute major depressive episode: analysis of heart rate dynamics , 2011, Translational Psychiatry.

[85]  Markus P. Schlaich,et al.  Change in Sympathetic Nerve Firing Pattern Associated with Dietary Weight Loss in the Metabolic Syndrome , 2011, Front. Physio..

[86]  L. Stankovic.  Transforming trauma: a qualitative feasibility study of integrative restoration (iRest) yoga Nidra on combat-related post-traumatic stress disorder. , 2011, International journal of yoga therapy.

[87]  P. Wändell,et al.  Increased heart rate variability but no effect on blood pressure from 8 weeks of hatha yoga – a pilot study , 2013, BMC Research Notes.

[88]  Samay Jain,et al.  Cardiovascular dysautonomia in Parkinson disease: From pathophysiology to pathogenesis , 2012, Neurobiology of Disease.

[89]  D. Ciraulo,et al.  Effects of yoga on the autonomic nervous system, gamma-aminobutyric-acid, and allostasis in epilepsy, depression, and post-traumatic stress disorder. , 2012, Medical hypotheses.

[90]  Luca Citi,et al.  A Real-Time Automated Point-Process Method for the Detection and Correction of Erroneous and Ectopic Heartbeats , 2012, IEEE Transactions on Biomedical Engineering.

[91]  R Furlan,et al.  Short-term complexity indexes of heart period and systolic arterial pressure variabilities provide complementary information. , 2012, Journal of applied physiology.

[92]  Junichiro Hayano,et al.  Non-Gaussianity of Low Frequency Heart Rate Variability and Sympathetic Activation: Lack of Increases in Multiple System Atrophy and Parkinson Disease , 2012, Front. Physio..

[93]  C. Gleissner.  Macrophage Phenotype Modulation by CXCL4 in Atherosclerosis , 2011, Front. Physio..

[94]  Michael Camilleri,et al.  The role of autonomic testing in the differentiation of Parkinson's disease from multiple system atrophy , 2012, Journal of the Neurological Sciences.

[95]  Valeria Iodice,et al.  Autonomic dysfunction in parkinsonian disorders: assessment and pathophysiology , 2012, Journal of Neurology, Neurosurgery & Psychiatry.

[96]  V. Roger.  Epidemiology of Heart Failure , 2013, Circulation research.

[97]  S. Tsai,et al.  Is mental illness complex? From behavior to brain , 2013, Progress in Neuro-Psychopharmacology and Biological Psychiatry.

[98]  R. Lu,et al.  Decreased Cardiac Vagal Control in Drug-Naïve Patients with Posttraumatic Stress Disorder , 2013, Psychiatry investigation.

[99]  Luca Citi,et al.  Instantaneous nonlinear assessment of complex cardiovascular dynamics by laguerre-volterra point process models , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[100]  Luca Citi,et al.  Point-Process Nonlinear Models With Laguerre and Volterra Expansions: Instantaneous Assessment of Heartbeat Dynamics , 2013, IEEE Transactions on Signal Processing.

[101]  C. Lonsdale,et al.  Effect of an office worksite-based yoga program on heart rate variability: outcomes of a randomized controlled trial , 2013, BMC Complementary and Alternative Medicine.

[102]  S. Mazza,et al.  Heart Rate and Heart Rate Variability Modification in Chronic Insomnia Patients , 2014, Behavioral sleep medicine.

[103]  V. Mohsenin,et al.  Diagnosis and management of sleep disorders in posttraumatic stress disorder:a review of the literature. , 2014, The primary care companion for CNS disorders.

[104]  David Emerson,et al.  Yoga as an adjunctive treatment for posttraumatic stress disorder: a randomized controlled trial. , 2014, The Journal of clinical psychiatry.

[105]  G Valenza,et al.  Point-process Nonlinear Autonomic Assessment of Depressive States in Bipolar Patients , 2014, Methods of Information in Medicine.

[106]  Luca Citi,et al.  Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics , 2014, PloS one.

[107]  E. Scilingo,et al.  Mood states modulate complexity in heartbeat dynamics: A multiscale entropy analysis , 2014 .

[108]  Luca Citi,et al.  Inhomogeneous point-process entropy: an instantaneous measure of complexity in discrete systems. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[109]  Eiichi Watanabe,et al.  MultiScale wavelet p-leader based heart rate variability analysis for survival probability assessment in CHF patients , 2014, 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[110]  P. Roche,et al.  Macropinocytosis in phagocytes: regulation of MHC class-II-restricted antigen presentation in dendritic cells , 2015, Front. Physiol..

[111]  Zhen Jin,et al.  Effects of time delay and space on herbivore dynamics: linking inducible defenses of plants to herbivore outbreak , 2015, Scientific Reports.

[112]  Leon Glass,et al.  Dynamical disease: Challenges for nonlinear dynamics and medicine. , 2015, Chaos.

[113]  Luca Citi,et al.  Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics , 2015, Front. Physiol..

[114]  Ulrike Goldschmidt,et al.  An Introduction To The Theory Of Point Processes , 2016 .

[115]  Luca Citi,et al.  Assessment of spontaneous cardiovascular oscillations in Parkinson's disease , 2016, Biomed. Signal Process. Control..

[116]  Zhen Jin,et al.  Periodic solutions in a herbivore-plant system with time delay and spatial diffusion , 2016 .