Insights from a discrete generalized beta distribution analysis of heart rate and blood pressure variability: an integrated approach to study end-stage renal disease

The study of inter-beat intervals (IBI) and systolic blood pressure (SBP) fluctuations is of public health importance. Here we obtain insights about their underlying dynamics by means of an innovative study of the distribution of their rank-ordered registers, provided by fits to the Discrete Generalized Beta Distribution (DGBD), for healthy subjects and patients with end-stage renal disease (ESRD), under an active standing maneuver. SBP and IBI non-invasive time series were recorded during supine position followed by active standing for nine ESRD patients and eighteen age-matched healthy subjects. Once the data were rank ordered, the three parameter DGBD function was fitted through the Levenberg-Marquardt non-linear algorithm. Taking into consideration the statistical interpretations of the parameters, the quantitative exploration of their dependence with regard to the cases examined and changes in body position provided new insights: (i) Evidence for the presence of regulatory mechanisms that preserve the tail symmetry of the IBI distributions in healthy subjects, which are not evident in ESRD patients; (ii) The identification of a more pronounced weight of low-magnitude fluctuations at active standing in the SBP time series, manifested as a broader statistical dispersion of blood pressure values; (iii) A quantitative determination of a more undermined SBP regulation in ESRD. Overall, a better understanding of the statistical behavior of IBI and SBP time series is achieved by means of the DGBD function. Through the variation of its parameters, the DGBD approach has the potential to become a marker for assessing or even predicting the impairment of cardiovascular control mechanisms.