Correlation dimension estimation: can this nonlinear description contribute to the characterization of blood pressure control in rats?

Abstract

The application of correlation dimension estimation to the study of cardiovascular control, via the blood pressure (BP) time series was investigated. We chose to calculate the Grassberger-Procaccia (GP) correlation dimension. In order to obtain a reliable estimate of the correlation dimension, we studied impact of various parameters such as the appropriate sampling rate, the time delays, the embedding dimension, the minimal trace length required, and the number of points needed as reference points. We developed a recipe for the reliable treatment of the continuous BP signal in rats, our animal model, and discussed the possible pitfalls which demand special attention. Next, we applied the surrogate data method to a BP time series, looking for the existence of nonlinear components, in order to test whether the nonlinear modeling is necessary for accurately describing the system. We found that, indeed, the correlation dimension does reveal information which cannot be unveiled by the commonly used power spectral technique, thus, making the nonlinear modeling an important approach, providing additional insight into the cardiovascular control system.