https://doi.org/10.1140/epjs/s11734-025-02074-0
Regular Article
Evaluating directionality via cross-predictability and cloud size ratio methods: application to cerebrovascular dynamic interactions during active orthostatism
1
Department of Biomedical Sciences for Health, University of Milan, 20133, Milan, Italy
2
Department of Cardiothoracic, Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, 20097, Milan, San Donato Milanese, Italy
3
IRCCS Istituti Clinici Scientifici Maugeri, 20138, Milan, Italy
a
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Received:
20
May
2025
Accepted:
18
November
2025
Published online:
1
December
2025
Abstract
We compare two different strategies for the evaluation of directionality based on state space correspondence (SSC) class, namely k-nearest neighbor cross-predictability (CP) and cloud size ratio (CSR) methods in the context of bivariate data. Several CSR approaches were considered. The techniques were applied to describe statistical dependences between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv) in 27 healthy volunteers (age: 44 ± 11 years; 14 females, 13 males) undergoing recordings at rest in the supine position (REST) and during active standing (STAND). A surrogate data approach was applied to check the null hypothesis of the absence of coupling. Over synthetic bivariate series generated by nonlinear stochastic interacting systems we found that only the CP technique was able to detect causality from the driver to the responder, while the performance of the CSR strategy was more limited. Over experimental data, we found that: (i) indexes computed via CP and CSR methods were significantly correlated, but correlation was weaker from MAP to MCBv; (ii) at REST closed loop MCBv-MAP dynamic interactions were detectable and they were more present during STAND; (iii) STAND increased the strength of the causal link from MAP to MCBv and vice versa. We conclude that the CP approach is more powerful than the CSR strategy in describing directionality of dynamic interactions even though values of the strength of the coupling computed by the two approaches are correlated and useful to describe the closed loop dependences between MAP and MCBv and the impact of the orthostatic challenge on them.
© The Author(s) 2025
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