title: Linearity and non-linearity in cerebral hemodynamics.
abstract: BACKGROUND
  Transcranial Doppler ultrasound has been extensively used to study cerebral hemodynamics, and yet the basic characteristics of the input/output system of blood pressure/velocity are little known. We examine whether this system can best be considered linear or non-linear.
  
  
  METHODS
  We assessed the adequacy of linear modeling in four ways: (1) Known properties of cerebral blood flow were reviewed and analyzed from a systems standpoint; (2) 1100 ARX & OE model types were tested with data from 29 normal subjects, with and without lowpass filtering; (3) time-frequency analysis was used to identify nonstationary behavior and markers of non-linearity (such as bifurcations, chirps, and intermittent autoregulatory impairment) in the same data sets; (4) simple computer models of autoregulation incorporating time delays and non-linear elements were tested for production of spontaneous oscillations.
  
  
  RESULTS
  (1) Several aspects of cerebral hemodynamics are poorly described by linear models, (2) the ARX & OE models performed poorly, (3) time-frequency analysis showed non-linear and nonstationary behavior, (4) the computer models produced spontaneous oscillations similar to those observed in humans.
  
  
  CONCLUSIONS
  There is strong evidence that the blood pressure/velocity system is non-linear.
authors.affiliation: The University of Texas Southwestern Medical Center, Department of Neurosurgery, 5323 Harry Hines Boulevard, Dallas, TX 75390-8855, USA. cole.giller@utsouthwestern.edu
authors.forename: Cole A
authors.initials: CA
authors.lastname: Giller
authors.forename: Martin
authors.initials: M
authors.lastname: Mueller
mesh_terms: D001783:Blood Flow Velocity; D001794:Blood Pressure; D001921:Brain / Q000098:blood supply* / Q000502:physiology*; D002560:Cerebrovascular Circulation / Q000502:physiology*; D003198:Computer Simulation; D004453:Echoencephalography / Q000379:methods; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D016014:Linear Models; D008297:Male; D020768:Middle Cerebral Artery / Q000000981:diagnostic imaging / Q000502:physiology; D008955:Models, Cardiovascular; D008959:Models, Neurological; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes