Multiscale Joint Symbolic Transfer Entropy for Quantification of Causal Interactions Between Heart Rate and Blood Pressure Variability Under Postural Stress
In this paper, joint symbolic transfer entropy (JSTE) is explored to quantify causal interactions between systolic blood pressure (SBP) and RR intervals (peak-to-peak distance between consecutive R-peaks) at multiple time scales. SBP→RR coupling (C s-r ) and RR→SBP coupling (C r-s ) coupling is analyzed at multiple time scales and delays. The ability of the approach based on JSTE to detect SBP–RR causal coupling is tested on 42 healthy subjects in supine and upright position along with 21 subjects of EUROBAVAR dataset. In addition, lack of causal coupling from SBP to RR was assessed on 20 post-acute myocardial infarction (AMI) patients. Results demonstrate that (i) standard deviation (SD) of RR interval series and SBP series decreases with time scale τ = 1 to 10 for all types of subjects. (ii) SD in supine is more than that of upright position at each time scale irrespective of types of subjects. (iii) JSTE decreases with time delay for healthy and AMI patients but does not follow decreasing trend for baroflex sensitivity BRS failure patients. (iv) JSTE in supine position is more than that of upright position irrespective of time delay. (v) JSTE decreases with time scale for healthy and AMI patients but does not follow decreasing trend for BRS failure patients. (vi) JSTE in supine position is more than that of upright position only at finer scales. (vii) Enhanced feed-forward (FF) coupling and suppressed feedback (FB) coupling found at supine position within low frequency band (0.04–0.15 Hz) as well as high frequency band (0.151–0.4 Hz) indicated prevalence on non-baroreflex mechanisms. (viii) FB coupling recovered in the upright position which was stronger than FF coupling. Upon comparison with cross conditional entropy (CCE), it is found that JSTE provides more significant differences between supine and upright position.