Causal coherence detects causality in the closed loop relationship between heart period and systolic arterial pressure variability series

Coherence is not able to evaluate the strength of the link between two interacting signals in a specific causal direction, as it merges both the feedback and the feedforward arms of the closed loop describing the relationships between them. We propose a method to evaluate the degree of linear dependency between two variables at each frequency without losing causality. It is based on the definition of two causal coherence functions. The approach is tested on the heart period and systolic arterial pressure beat-to-beat series recorded in seven heart-transplant recipients less than 14 months after the transplantation. In healthy subjects, these variables interact in a closed loop, but in heart-transplant recipients, the neural feedback path (from arterial pressure to heart period) is cut due to the surgical procedure, while the mechanical path (from heart period to arterial pressure) is preserved. The significance of the coupling is assessed by means of a surrogate data approach