title: Description of the ventriculoarterial interaction dynamics using recurrence plot strategies.
abstract: OBJECTIVE
  The classical description of ventriculoarterial coupling by calculating the ratio between the effective arterial elastance Ea to the end-systolic elastance Ees does not give insight into the underlying dynamics of the interaction between left-ventricular pressure (LVP) and aortic pressure (AOP) and flow (AOF). The aim of this study was to introduce a state space representation for the ventriculoarterial coupling and to quantify changes of the coupling state.
  
  
  METHODS
  A ventriculoarterial state space orbit VAO was defined to be dependent on three variables: VAO = [LVP(t), AOP(t + delta t), AOF(t + delta t)]. Changes in the coupling effect directly or indirectly on the time series of these parameters. They reflect the actual state of the cardiovascular system. The time delay delta t between the LVP and the aortic signals takes respect to the short delay between the heart action and the resulting waves in the arterial tree. The recurrence map of the VAO(i) (i = 1 .. N, N = number of points) is constructed by plotting the index i of every single point on the orbit (x-axis) against the indices of his 10 nearest neighbors (y-axis) in distance. The data were recorded in 9 anaesthetized pigs with a sample frequency of 512 Hz over a period of 6 seconds using piezoelectric pressure sensors and a Doppler flowmeter. A control condition was compared to a total occlusion of the descending aorta as a strong artificial disturbance of ventriculoarterial interaction. The nonlinear parameters percent recurrence, percent determinism and the entropy were calculated from the plot.
  
  
  RESULTS
  Periodic crossing points and forbidden zones in all plots identify the nonlinear character of the chosen variables. The recurrent patterns are less rigid for control conditions than for total occlusion. Entropy (2.3% rise) and determinism (24% rise) are significantly (p < 0.003) increased. Total aortic occlusion leads to more complex time correlation patterns.
  
  
  CONCLUSIONS
  These results may reflect the loss of an ideal coupling state leading to a more complex deterministic behavior of the overall regulatory system. Because recurrence plots do not impose rigid constraints on data set size, stationarity, or statistical distribution, we hypothesize that this technique might be useful to describe the nonlinear dynamics between left ventricle and arterial system.
authors.affiliation: Dept. of Cardiac Surgery, University of Heidelberg, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Schulz
authors.forename: R
authors.initials: R
authors.lastname: Bauernschmitt
authors.forename: A
authors.initials: A
authors.lastname: Schwarzhaupt
authors.forename: C F
authors.initials: CF
authors.lastname: Vahl
authors.forename: U
authors.initials: U
authors.lastname: Kiencke
mesh_terms: D000818:Animals; D001013:Aorta, Thoracic / Q000502:physiology; D001158:Arteries / Q000502:physiology*; D003250:Constriction; D004548:Elasticity; D006439:Hemodynamics; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D013552:Swine; D016277:Ventricular Function, Left; D017725:Ventricular Pressure