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In this work, we study ultra-short term (UST) complexity of Heart Rate Variability (HRV) and its agreement with analysis of standard short-term (ST) HRV recordings obtained at rest and during orthostatic stress. Conditional Entropy (CE) measures have been computed using both a linear Gaussian approximation and a more accurate model-free approach based on nearest neighbors. The agreement between UST and ST indices has been compared via statistical tests and correlation analysis, suggesting the feasibility of exploiting faster algorithms and shorter time series for detecting changes in cardiovascular control during various states.

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see text]. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.

Brain plasticity and functional reorganization are mechanisms behind functional motor recovery of patients after an ischemic stroke. The study of resting-state motor network functional connectivity by means of EEG proved to be useful in investigating changes occurring in the information flow and find correlation with motor function recovery. In the literature, most studies applying EEG to post-stroke patients investigated the undirected functional connectivity of interacting brain regions. Quite recently, works started to investigate the directionality of the connections and many approaches or features have been proposed, each of them being more suitable to describe different aspects, e.g., direct or indirect information flow between network nodes, the coupling strength or its characteristic oscillation frequency. Each work chose one specific measure, despite in literature there is not an agreed consensus, and the selection of the most appropriate measure is still an open issue. In an attempt to shed light on this methodological aspect, we propose here to combine the information of direct and indirect coupling provided by two frequency-domain measures based on Granger’s causality, i.e., the directed coherence (DC) and the generalized partial directed coherence (gPDC), to investigate the longitudinal changes of resting-state directed connectivity associated with sensorimotor rhythms α and β, occurring in 18 sub-acute ischemic stroke patients who followed a rehabilitation treatment. Our results showed a relevant role of the information flow through the pre-motor regions in the reorganization of the motor network after the rehabilitation in the sub-acute stage. In particular, DC highlighted an increase in intra-hemispheric coupling strength between pre-motor and primary motor areas, especially in ipsi-lesional hemisphere in both α and β frequency bands, whereas gPDC was more sensitive in the detection of those connection whose variation was mostly represented within the population. A decreased causal flow from contra-lesional premotor cortex towards supplementary motor area was detected in both α and β frequency bands and a significant reinforced inter-hemispheric connection from ipsi to contra-lesional pre-motor cortex was observed in β frequency. Interestingly, the connection from contra towards ipsilesional pre-motor area correlated with upper limb motor recovery in α band. The usage of two different measures of directed connectivity allowed a better comprehension of those coupling changes between brain motor regions, either direct or mediated, which mostly were influenced by the rehabilitation, revealing a particular involvement of the pre-motor areas in the cerebral functional reorganization.