Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by mainly redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone

Categorizing the Role of Respiration in Cardiovascular and Cerebrovascular Variability Interactions

Objective: Respiration disturbs cardiovascular and cerebrovascular controls but its role is not fully elucidated. Methods: Respiration can be classified as a confounder if its observation reduces the strength of the causal relationship from source to target. Respiration is a suppressor if the opposite situation holds. We prove that a confounding/suppression (C/S) test can be accomplished by evaluating the sign of net redundancy/synergy balance in the predictability framework based on multivariate autoregressive modelling. In addition, we suggest that, under the hypothesis of Gaussian processes, the C/S test can be given in the transfer entropy decomposition framework as well. Experimental protocols: We applied the C/S test to variability series of respiratory movements, heart period, systolic arterial pressure, mean arterial pressure, and mean cerebral blood flow recorded in 17 pathological individuals (age: 648 yrs; 17 males) before and after induction of propofol-based general anesthesia prior to coronary artery bypass grafting, and in 13 healthy subjects (age: 278 yrs; 5 males) at rest in supine position and during head-up tilt with a table inclination of 60. Results: Respiration behaved systematically as a confounder for cardiovascular and cerebrovascular controls. In addition, its role was affected by propofol-based general anesthesia but not by a postural stimulus of limited intensity. Conclusion: The C/S test can be fruitfully exploited to categorize the role of respiration over causal variability interactions. Significance: The application of the C/S test could favor the comprehension of the role of respiration in cardiovascular and cerebrovascular regulations

Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks

Objective: Indexes assessing the balance between redundancy and synergy were hypothesized to be helpful in characterizing cardiovascular control from spontaneous beat-to-beat variations of heart period (HP), systolic arterial pressure (SAP), and respiration (R). Methods: Net redundancy/synergy indexes were derived according to predictability and transfer entropy decomposition strategies via a multivariate linear regression approach. Indexes were tested in two protocols inducing modifications of the cardiovascular regulation via baroreflex loading/unloading (i.e., head-down tilt at -25° and graded head-up tilt at 15°, 30°, 45°, 60°, 75°, and 90°, respectively). The net redundancy/synergy of SAP and R to HP and of HP and R to SAP were estimated over stationary sequences of 256 successive values. Results: We found that: 1) regardless of the target (i.e., HP or SAP) redundancy was prevalent over synergy and this prevalence was independent of type and magnitude of the baroreflex challenge; 2) the prevalence of redundancy disappeared when decoupling inputs from output via a surrogate approach; 3) net redundancy was under autonomic control given that it varied in proportion to the vagal withdrawal during graded head-up tilt; and 4) conclusions held regardless of the decomposition strategy. Conclusion: Net redundancy indexes can monitor changes of cardiovascular control from a perspective completely different from that provided by more traditional univariate and multivariate methods. Significance: Net redundancy measures might provide a practical tool to quantify the reservoir of effective cardiovascular regulatory mechanisms sharing causal influences over a target variable