Abstract: G. H. González-Gómez, O. Infante, P. Martánez-García, C. Lerma (2018)

The inter beat interval (IBI) duration and systolic blood pressure (SBP) are cardiovascular variables related through several feedback mechanisms. We propose the analysis of diagonal lines in cross recurrence plots (CRPs) from IBI and SBP embedded within the same phase space to identify events where trajectories of both variables concur. The aim of the study was to describe the relationship between IBI and SBP of healthy subjects using CRP and diagonal analysis during baseline condition – supine position (SP) – and how the relationship changes during the physiological stress of active standing (AS). IBI and SBP time series were obtained from continuous blood pressure recordings during SP and AS (15 min each) in 19 young healthy subjects. IBI and SBP time series were embedded within a five-dimensional phase space using an embedding delay estimated from cross correlation between IBI and SBP. During SP, mean CRP showed high determinism (≥85%) and also brief but repeated events where both variables stay within a reduced space. Most quantitative recurrences analysis indexes of CRP increased significantly (p<0.05) during AS. CRP analysis showed short diagonals indicating a very strong deterministic relationship between IBI and SBP with intermittent unlocking periods. The strength of IBI and SBP relationship increased during the physiological stress of AS. The CRP method allowed a rigorous quantitative description of the deterministic association between these two variables. Diagonal lines were intermittent and not always parallel, showing that there is not a defined and unique rhythm. This suggests the activation of different influences at different times and with different precedence between the heart rate and blood pressure in response to AS.
The heart rate and blood pressure are representative variables of the cardiovascular system, and time series analysis of beat to beat variations in these variables has helped one to understand many cardiovascular regulation mechanisms. However, the complex nonlinear interactions within these variables are not fully understood. Here such interactions were characterized through embedding of their respective discrete time series within the same phase space and identification of all events where their trajectories concur (cross recurrence plot). This revealed a very strong deterministic relationship, in which both variables synchronize frequently but during relatively short periods, and with continuous switching in the order of precedence at different lags. Inducing physiological stress by active standing strengthens their interaction. This is consistent with the concept of the cardiovascular control as a nonlinear feedback system and improves the understanding of the interaction between these two variables.

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Analysis of diagonals in cross recurrence plots between heart rate and systolic blood pressure during supine position and active standing in healthy adults