Cardiovascular Dependency Structures: Transformation to Temporal Domain

Copula is a (cumulative) distribution function with a density that visualizes the dependency structure of two or more time series. Frank's copula is well suited for systolic blood pressure (SBP) and pulse interval (PI) signal pairs, but the copula analyses are restricted to the probabilistic domain. A new, single-dimensional, time series that reflects the fluctuations of the signal dependency level can be obtained by mapping the signal coupling strength at a beat-by-beat basis. Such a transformation requires a probability density estimation. This paper compares several methods of density estimation to produce a time series that correspond to the dependency fluctuation of SBP and PI time series. As an illustrative example, vasopressin selective V1a and V2 receptor antagonists were employed to modulate simultaneously multiple physiological functions.