title: Estimation of instantaneous complex dynamics through Lyapunov exponents: a study on heartbeat dynamics.
abstract: Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations.
authors.affiliation: Neuroscience Statistics Research Laboratory, Department of Anesthesia, Critical Care & Pain Medicine, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts, United States of America; and Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America; Research Center E. Piaggio and Department of Information Engineering, University of Pisa, Pisa, Italy.
authors.forename: Gaetano
authors.initials: G
authors.lastname: Valenza
authors.affiliation: Neuroscience Statistics Research Laboratory, Department of Anesthesia, Critical Care & Pain Medicine, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts, United States of America; and Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America; School of Computer Science and Electronic Engineering, University of Essex, Colchester, United Kingdom.
authors.forename: Luca
authors.initials: L
authors.lastname: Citi
authors.affiliation: Neuroscience Statistics Research Laboratory, Department of Anesthesia, Critical Care & Pain Medicine, Harvard Medical School, Massachusetts General Hospital, Boston, Massachusetts, United States of America; and Department of Brain and Cognitive Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.
authors.forename: Riccardo
authors.initials: R
authors.lastname: Barbieri
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004562:Electrocardiography / Q000379:methods; D006321:Heart / Q000502:physiology*; D006333:Heart Failure / Q000175:diagnosis / Q000503:physiopathology*; D006339:Heart Rate / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes