title: Multiscale Poincaré plots for visualizing the structure of heartbeat time series.
abstract: BACKGROUND
  Poincaré delay maps are widely used in the analysis of cardiac interbeat interval (RR) dynamics. To facilitate visualization of the structure of these time series, we introduce multiscale Poincaré (MSP) plots.
  
  
  METHODS
  Starting with the original RR time series, the method employs a coarse-graining procedure to create a family of time series, each of which represents the system's dynamics in a different time scale. Next, the Poincaré plots are constructed for the original and the coarse-grained time series. Finally, as an optional adjunct, color can be added to each point to represent its normalized frequency.
  
  
  RESULTS
  We illustrate the MSP method on simulated Gaussian white and 1/f noise time series. The MSP plots of 1/f noise time series reveal relative conservation of the phase space area over multiple time scales, while those of white noise show a marked reduction in area. We also show how MSP plots can be used to illustrate the loss of complexity when heartbeat time series from healthy subjects are compared with those from patients with chronic (congestive) heart failure syndrome or with atrial fibrillation.
  
  
  CONCLUSIONS
  This generalized multiscale approach to Poincaré plots may be useful in visualizing other types of time series.
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. teresa.henriques@wyss.harvard.edu.| Center for Anesthesia Research and Excellence (CARE), Beth Israel Deaconess Medical Center, Boston, MA, USA. teresa.henriques@wyss.harvard.edu.|Margret and H.A. Rey Institute of Nonlinear Dynamics in Physiology and Medicine, Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center, Boston, MA, USA. teresa.henriques@wyss.harvard.edu.
authors: Teresa S
authors: TS
authors: Henriques
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. sara.mariani@wyss.harvard.edu.|Division of Sleep and Circadian Disorders, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA. sara.mariani@wyss.harvard.edu.
authors: Sara
authors: S
authors: Mariani
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. burykin@gmail.com.
authors: Anton
authors: A
authors: Burykin
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. filipacsrodrigues@gmail.com.|Department of Physics, Faculty of Sciences, University of Lisbon, Lisbon, Portugal. filipacsrodrigues@gmail.com.
authors: Filipa
authors: F
authors: Rodrigues
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. tiagosilva_8@hotmail.com.|Department of Physics, Faculty of Sciences, University of Lisbon, Lisbon, Portugal. tiagosilva_8@hotmail.com.
authors: Tiago F
authors: TF
authors: Silva
authors: Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA. agoldber@bidmc.harvard.edu.|Margret and H.A. Rey Institute of Nonlinear Dynamics in Physiology and Medicine, Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center, Boston, MA, USA. agoldber@bidmc.harvard.edu.
authors: Ary L
authors: AL
authors: Goldberger
mesh_terms: D001281:Atrial Fibrillation / Q000503:physiopathology; D003627:Data Interpretation, Statistical; D006333:Heart Failure / Q000503:physiopathology; D006339:Heart Rate / Q000502:physiology*; D006801:Humans; D015233:Models, Statistical