Copula as a dynamic measure of cardiovascular signal interactions

Abstract

Objectives: Copula is a tool for measuring linear and non-linear interactions between two or more time series. The aim of this paper is to prove that a copula approach can accurately capture and visualize the spatial and temporal fluctuations in dependency structures of cardiovascular signals, and to outline the application possibilities. Methods: The method for measuring the level of interaction between systolic blood pressure and the corresponding pulse interval is validated statistically and pharmacologically. The time series are recorded from the freely moving male Wistar rats equipped with radio-telemetry device for blood pressure recording, before and after administration of autonomic blockers scopolamine, atenolol, prazosin and hexamethonium. Implicit (Gaussian and t) and explicit (Clayton, Frank and Gumbel) copulas were calculated and compared to the conventional bivariate methods (Kendal, Pearson, Spearman and classical correlation). Further statistical validation was done using artificially generated surrogate data. A window sliding procedure for dynamic monitoring the signals' coupling strength is implemented. Results: Under the baseline physiological conditions, SBP-PI dependency is significant for time lags 0 s-4 s. Hexamethonium completely abolished the dependency, scopolamine abolished it for time lags 0 s-2 s, atenolol first slightly increased, than for lags greater than 2 s decreased the dependency and prazosin had no effect. Isospectral and isodistributional surrogate data tests confirm that copulas successfully notify the absence of dependency as well. Conclusion: Copula approach accurately captures the temporal fluctuations in dependency structures of SBP and PI, simultaneously enabling a visualization of dependency levels within the particular signal zones. An analysis showed that copulas are more sensitive than the conventional statistical measures, with Frank copula exhibiting the best characterization of SBP and PI dependency.