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

A. Porta, V. Bari, B. De Maria, A.C.M. Takahashi, S. Guzzetti, R. Colombo, A.M. Catai, F. Raimondi, L. Faes

Research output: Contribution to journalArticlepeer-review


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. © 1964-2012 IEEE.
Original languageEnglish
Pages (from-to)2628-2638
Number of pages11
JournalIEEE Transactions on Biomedical Engineering
Issue number11
Publication statusPublished - 2017


  • Autonomic nervous system
  • cardiovascular control
  • head-down tilt (HDT)
  • head-up tilt (HUT)
  • heart rate variability
  • Wiener-Granger causality
  • Entropy
  • Cardiovascular control
  • Granger Causality
  • Head-up tilts
  • Heart rate variability
  • Redundancy
  • adult
  • aged
  • arterial pressure
  • Article
  • autonomic nervous system
  • breathing
  • cardiovascular parameters
  • decomposition
  • entropy
  • extrasystole
  • female
  • head-down tilt
  • heart cycle
  • human
  • kernel method
  • limit of quantitation
  • male
  • net redundancy
  • normal human
  • pressoreceptor reflex
  • prevalence
  • QRS complex
  • redundancy analysis
  • systolic arterial pressure
  • thorax pressure


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