Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ϵ-recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.

[1]  C. Smith.  Diagnostic tests (1) – sensitivity and specificity , 2012, Phlebology.

[2]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[4]  C. Li,et al.  Evolving model of amino acid networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Raúl Toral,et al.  Nonequilibrium transitions in complex networks: a model of social interaction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  C. Juel.  Über einige Grundgebilde der projectiven Geometrie , 1890 .

[7]  Stephen B. Seidman,et al.  Network structure and minimum degree , 1983 .

[8]  Norbert Marwan,et al.  The geometry of chaotic dynamics — a complex network perspective , 2011, 1102.1853.

[9]  T. S. Evans,et al.  Complex networks , 2004 .

[10]  Markus Porto,et al.  Multicomponent reaction-diffusion processes on complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  D. Eckberg,et al.  Arterial Baroreflexes and Cardiovascular Modeling , 2008, Cardiovascular engineering.

[12]  Lucas Lacasa,et al.  Description of stochastic and chaotic series using visibility graphs. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Vladimir Batagelj,et al.  An O(m) Algorithm for Cores Decomposition of Networks , 2003, ArXiv.

[14]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[15]  Ruben Juanes,et al.  Anomalous physical transport in complex networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Douglas Maraun,et al.  Nonlinear Processes in Geophysics , 2000 .

[17]  Ramakrishna Mukkamala,et al.  System identification: a multi-signal approach for probing neural cardiovascular regulation , 2005, Physiological measurement.

[18]  Giuseppe Baselli,et al.  Multimodal signal processing for the analysis of cardiovascular variability , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[20]  Michael Small,et al.  Superfamily phenomena and motifs of networks induced from time series , 2008, Proceedings of the National Academy of Sciences.

[21]  Jm Roberts,et al.  Pathogenesis and genetics of pre-eclampsia , 2001, The Lancet.

[22]  T Penzel,et al.  Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Percy C. Magnus,et al.  Seasonal variation in the occurrence of pre‐eclampsia , 2001, BJOG : an international journal of obstetrics and gynaecology.

[24]  George Sugihara,et al.  Detecting Causality in Complex Ecosystems , 2012, Science.

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

[26]  R. Levine,et al.  Sequential Changes in Antiangiogenic Factors in Early Pregnancy and Risk of Developing Preeclampsia , 2007 .

[27]  J. Kurths,et al.  Nonlinear analysis of complex phenomena in cardiological data , 2000, Herzschrittmachertherapie und Elektrophysiologie.

[28]  E. Mohammadi,et al.  Barriers and facilitators related to the implementation of a physiological track and trigger system: A systematic review of the qualitative evidence , 2017, International journal for quality in health care : journal of the International Society for Quality in Health Care.

[29]  James J. Walker,et al.  Pre-eclampsia , 2000, The Lancet.

[30]  J. Taylor,et al.  Short‐term cardiovascular oscillations in man: measuring and modelling the physiologies , 2002, The Journal of physiology.

[31]  P. Castiglioni,et al.  Baroreflex contribution to blood pressure and heart rate oscillations: time scales, time-variant characteristics and nonlinearities , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[32]  A Voss,et al.  Analysis of cardiovascular oscillations: a new approach to the early prediction of pre-eclampsia. , 2007, Chaos.

[33]  S. Cnattingius,et al.  Tobacco Use During Pregnancy and Preeclampsia Risk: Effects of Cigarette Smoking and Snuff , 2010, Hypertension.

[34]  D. Altman,et al.  Statistics Notes: Diagnostic tests 2: predictive values , 1994, BMJ.

[35]  Jürgen Kurths,et al.  Ambiguities in recurrence-based complex network representations of time series. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  S. Blackwell,et al.  Angiotensin Receptor Agonistic Autoantibody Is Highly Prevalent in Preeclampsia: Correlation With Disease Severity , 2010, Hypertension.

[37]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[38]  A. Porta,et al.  Accounting for Respiration is Necessary to Reliably Infer Granger Causality From Cardiovascular Variability Series , 2012, IEEE Transactions on Biomedical Engineering.

[39]  K. Chon,et al.  Respiratory sinus arrhythmia: opposite effects on systolic and mean arterial pressure in supine humans , 2001, The Journal of physiology.

[40]  Jürgen Kurths,et al.  Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution , 2011, Proceedings of the National Academy of Sciences.

[41]  D. Altman,et al.  Statistics Notes: Diagnostic tests 1: sensitivity and specificity , 1994 .

[42]  J. Kurths,et al.  Complex network approach for recurrence analysis of time series , 2009, 0907.3368.

[43]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[44]  Julio M. Ottino,et al.  Complex networks , 2004, Encyclopedia of Big Data.

[45]  N. Wessel,et al.  Predictive Value of Maternal Angiogenic Factors in Second Trimester Pregnancies With Abnormal Uterine Perfusion , 2007, Hypertension.

[46]  J. Kurths,et al.  Synchronization in networks of mobile oscillators. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  J. Gilbert,et al.  Approaching the threshold for predicting preeclampsia: monitoring angiogenic balance during pregnancy. , 2011, Hypertension.

[48]  Marie Brown,et al.  Robust Early Pregnancy Prediction of Later Preeclampsia Using Metabolomic Biomarkers , 2010, Hypertension.

[49]  D. Maulik,et al.  Doppler Velocimetry for Fetal Surveillance: Randomized Clinical Trials and Implications for Practice , 2005 .

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

[51]  J. Zbilut,et al.  Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals. , 2002, Medical engineering & physics.

[52]  J. Kurths,et al.  Quantitative analysis of heart rate variability. , 1995, Chaos.

[53]  Hagen Malberg,et al.  Nonlinear Methods of Cardiovascular Physics and their Clinical Applicability , 2007, Int. J. Bifurc. Chaos.

[54]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[55]  S Battiston,et al.  Backbone of complex networks of corporations: the flow of control. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[56]  Michael Small,et al.  Recurrence-based time series analysis by means of complex network methods , 2010, Int. J. Bifurc. Chaos.

[57]  Jürgen Kurths,et al.  Recurrence networks—a novel paradigm for nonlinear time series analysis , 2009, 0908.3447.

[58]  Niels Wessel,et al.  Short-term couplings of the cardiovascular system in pregnant women suffering from pre-eclampsia , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[59]  Ulrich Parlitz,et al.  Probabilistic evaluation of time series models: a comparison of several approaches. , 2009, Chaos.

[60]  André Longtin,et al.  Review and classification of variability analysis techniques with clinical applications , 2011, Biomedical engineering online.

[61]  T. Schreiber.  Interdisciplinary application of nonlinear time series methods , 1998, chao-dyn/9807001.

[62]  Mitsuaki Suzuki,et al.  Threshold of Soluble Fms-Like Tyrosine Kinase 1/Placental Growth Factor Ratio for the Imminent Onset of Preeclampsia , 2011, Hypertension.

[63]  P. McClintock,et al.  Nonlinear dynamics of cardiovascular ageing , 2010, Physics reports.

[64]  F. Légaré,et al.  Combining biochemical and ultrasonographic markers in predicting preeclampsia: a systematic review. , 2010, Clinical chemistry.

[65]  L. Poston,et al.  Urinary Proteomics for Prediction of Preeclampsia , 2011, Hypertension.

[66]  Karel H Wesseling,et al.  Variability in Cardiovascular Control: The Baroreflex Reconsidered , 2008, Cardiovascular engineering.

[67]  Hagen Malberg,et al.  A combined technique for predicting pre-eclampsia: concurrent measurement of uterine perfusion and analysis of heart rate and blood pressure variability , 2006, Journal of hypertension.

[68]  N. Wessel,et al.  Circulatory soluble endoglin and its predictive value for preeclampsia in second-trimester pregnancies with abnormal uterine perfusion. , 2008, American journal of obstetrics and gynecology.