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 journalArticle

5 Citations (Scopus)

Abstract

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
Volume64
Issue number11
DOIs
Publication statusPublished - 2017

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Redundancy
Entropy
Decomposition
Unloading
Linear regression

Keywords

  • 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

Cite this

Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks. / Porta, A.; Bari, V.; De Maria, B.; Takahashi, A.C.M.; Guzzetti, S.; Colombo, R.; Catai, A.M.; Raimondi, F.; Faes, L.

In: IEEE Transactions on Biomedical Engineering, Vol. 64, No. 11, 2017, p. 2628-2638.

Research output: Contribution to journalArticle

@article{a4544699d1894f07a2e1b30e37c787d5,
title = "Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks",
abstract = "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. {\circledC} 1964-2012 IEEE.",
keywords = "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",
author = "A. Porta and V. Bari and {De Maria}, B. and A.C.M. Takahashi and S. Guzzetti and R. Colombo and A.M. Catai and F. Raimondi and L. Faes",
note = "Cited By :1 Export Date: 2 March 2018 CODEN: IEBEA Correspondence Address: Porta, A.; Department of Biomedical Sciences for Health, University of MilanItaly; email: alberto.porta@unimi.it References: Faes, L., Predictability decomposition detects the impairment of brain-heart dynamical networks during sleep disorders and their recovery with treatment (2016) Philosoph. Trans. Roy. Soc. Amer., 374; Porta, A., Disentangling cardiovascular control mechanisms during head-down tilt via joint transfer entropy and self-entropy decompositions (2015) Front. Physiol., 6; Faes, L., Information decomposition in bivariate systems: Theory and application to cardiorespiratory dynamics (2015) Entropy, 17, pp. 277-303; Porta, A., Conditional self-entropy and conditional joint transfer entropy in heart period variability during graded postural challenge (2015) PLoS ONE, 10; Angelini, L., Redundant variables and Granger causality (2010) Phys. Rev. e, 81; Stramaglia, S., Synergy and redundancy in the Granger causal analysis of dynamical networks (2014) New J. Phys., 16; Barrett, A.B., Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems (2015) Phys. Rev. e, 91; Stramaglia, S., Expanding the transfer entropy to identify information circuits in complex systems (2012) Phys. Rev. e, 86; Cohen, M.A., Taylor, J.A., Short-term cardiovascular oscillations in man: Measuring and modelling the physiologies (2002) J. Physiol., 542, pp. 669-683; Koepchen, H.P., Neurophysiological background of central neural cardiovascular-respiratory coordination: Basic remarks and experimental approach (1981) J. Auton. Nervous Syst., 3, pp. 335-368; Porta, A., Effects of variations of the complexity of the target on the assessment of Wiener-Granger causality in cardiovascular control indexes (2016) Physiol. Meas., 37, pp. 276-290; Goldberger, A.L., Non-linear dynamics for clinicians: Chaos theory, fractals and complexity at the bedside (1996) Lancet, 347, pp. 1312-1314; Porta, A., Causal relationships between heart period and systolic arterial pressure during graded head-up tilt (2011) Amer. J. Physiol., 300, pp. R378-R386; Soderstrom, T., Stoica, P., (1988) System Identification, , Englewood Cliffs, NJ, USA: Prentice Hall; McEliece, R.J., (2002) The Theory of Information and Coding, , Cambridge, U. K. : Cambridge Univ. Press; Porta, A., Are nonlinear model-free conditional entropy approaches for the assessment of cardiac control complexity superior to the linear model-based one (2016) IEEE Trans. Biomed. Eng.; Andrzejak, R.G., Bivariate surrogate techniques: Necessity, strengths, and caveats (2003) Phys. Rev. e, 68; Eckberg, D.L., Temporal response patterns of the human sinus node to brief carotid baroreceptor stimuli (1976) J. Physiol., 258, pp. 769-782; Baselli, G., Model for the assessment of heart period and arterial pressure variability interactions and respiratory influences (1994) Med. Biol. Eng. Comput., 32, pp. 143-152; Porta, A., Accounting for respiration is necessary to reliably infer Granger causality from cardiovascular variability series (2012) IEEE Trans. Biomed. Eng., 59 (3), pp. 832-841. , Mar; Porta, A., Model-based assessment of baroreflex and cardiopulmonary couplings during graded head-up tilt (2012) Comput. Biol. Med., 42, pp. 298-305; Baselli, G., Spectral decomposition in multichannel recordings based on multivariate parametric identification (1997) IEEE Trans. Biomed. Eng., 44 (11), pp. 1092-1101. , Nov; Akaike, H., A new look at the statistical novel identification (1974) IEEE Trans. Autom. Control, 19 (6), pp. 716-723. , Dec; Faes, L., Mutual non linear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategies based on k nearest neighbors (2008) Phys. Rev. e, 78; Harder, M., Bivariate measure of redundant information (2013) Phys. Rev. e, 87; Griffith, V., Intersection information based on common randomness (2014) Entropy, 16, pp. 1985-2000; Bertschinger, N., Quantifying unique information (2014) Entropy, 16, pp. 2161-2183; Xiao, X., System identification: Amulti-signal approach for probing neural cardiovascular regulation (2005) Physiol. Meas., 26, pp. R41-R71; Cooke, W.H., Human responses to upright tilt: A window on central autonomic integration (1999) J. Physiol., 517, pp. 617-628; Montano, N., Power spectrum analysis of heart rate variability to assess changes in sympatho-vagal balance during graded orthostatic tilt (1994) Circulation, 90, pp. 1826-1831; Porta, A., Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability (2007) Amer. J. Physiol., 293, pp. H702-H708; Marchi, A., Calibrated variability of muscle sympathetic nerve activity during graded head-up tilt in humans and its link with noradrenaline data and cardiovascular rhythms (2016) Amer. J. Physiol., 310, pp. R1134-R1143; Furlan, R., Oscillatory patterns in sympathetic neural discharge and cardiovascular variables during orthostatic stimulus (2000) Circulation, 101, pp. 886-892; Faes, L., Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy (2013) Auton. Neurosci., Basic Clin., 178, pp. 76-82; Heart rate variability-Standards of measurement, physiological interpretation and clinical use (1996) Circulation, 93, pp. 1043-1065. , Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology; Porta, A., Short-term complexity indexes of heart period and systolic arterial pressure variabilities provide complementary information (2012) J. Appl. Physiol., 113, pp. 1810-1820; Saul, J.P., Transfer function analysis of the circulation: Unique insights into cardiovascular regulation (1991) Amer. J. Physiol., 261, pp. H1231-H1245; Mullen, T.J., System identification of closed loop cardiovascular control: Effects of posture and autonomic blockade (1997) Amer. J. Physiol., 272, pp. H448-H461; Nikias, L., Raghuveer, M.R., Bispectrum estimation: A digital signal processing framework (1987) Proc. IEEE, 75 (7), pp. 869-891. , Jul; Nakamura, T., Multiscale analysis of intensive longitudinal biomedical signals and its clinical applications (2016) Proc. IEEE, 104 (2), pp. 242-261. , Feb; Peng, C.-K., Long-range anticorrelations and non-Gaussian behavior of the heartbeat (1993) Phys. Rev. Lett., 70, pp. 1343-1346; Porta, A., Faes, L., Wiener-Granger causality in network physiology with applications to cardiovascular control and neuroscience (2016) Proc. IEEE, 104 (2), pp. 282-309. , Feb; Timme, N., Synergy, redundancy, andmultivariate informationmeasures: An experimentalist's perspective (2014) J. Comput. Neurosci., 36, pp. 119-140; Papana, A., Simulation study of direct causality measures in multivariate time series (2013) Entropy, 15, pp. 2635-2661; Faes, L., Linear and nonlinear analysis of brain-heart and brain-brain interactions during sleep (2015) Phys. Meas., 36, pp. 683-698; Voss, A., The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death (1996) Cardiovasc. Res., 31, pp. 419-433; Wessel, N., Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates (2000) Phys. Rev. e, 61, pp. 733-739; Barrett, A.B., Multivariate Granger causality and generalized variance (2010) Phys. Rev. e, 81; Muller, A., Causality in physiological signals (2016) Physiol. Meas., 37, pp. R46-R72",
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doi = "10.1109/TBME.2017.2654509",
language = "English",
volume = "64",
pages = "2628--2638",
journal = "IEEE Transactions on Biomedical Engineering",
issn = "0018-9294",
publisher = "IEEE Computer Society",
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TY - JOUR

T1 - Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks

AU - Porta, A.

AU - Bari, V.

AU - De Maria, B.

AU - Takahashi, A.C.M.

AU - Guzzetti, S.

AU - Colombo, R.

AU - Catai, A.M.

AU - Raimondi, F.

AU - Faes, L.

N1 - Cited By :1 Export Date: 2 March 2018 CODEN: IEBEA Correspondence Address: Porta, A.; Department of Biomedical Sciences for Health, University of MilanItaly; email: alberto.porta@unimi.it References: Faes, L., Predictability decomposition detects the impairment of brain-heart dynamical networks during sleep disorders and their recovery with treatment (2016) Philosoph. Trans. Roy. Soc. Amer., 374; Porta, A., Disentangling cardiovascular control mechanisms during head-down tilt via joint transfer entropy and self-entropy decompositions (2015) Front. Physiol., 6; Faes, L., Information decomposition in bivariate systems: Theory and application to cardiorespiratory dynamics (2015) Entropy, 17, pp. 277-303; Porta, A., Conditional self-entropy and conditional joint transfer entropy in heart period variability during graded postural challenge (2015) PLoS ONE, 10; Angelini, L., Redundant variables and Granger causality (2010) Phys. Rev. e, 81; Stramaglia, S., Synergy and redundancy in the Granger causal analysis of dynamical networks (2014) New J. Phys., 16; Barrett, A.B., Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems (2015) Phys. Rev. e, 91; Stramaglia, S., Expanding the transfer entropy to identify information circuits in complex systems (2012) Phys. Rev. e, 86; Cohen, M.A., Taylor, J.A., Short-term cardiovascular oscillations in man: Measuring and modelling the physiologies (2002) J. Physiol., 542, pp. 669-683; Koepchen, H.P., Neurophysiological background of central neural cardiovascular-respiratory coordination: Basic remarks and experimental approach (1981) J. Auton. Nervous Syst., 3, pp. 335-368; Porta, A., Effects of variations of the complexity of the target on the assessment of Wiener-Granger causality in cardiovascular control indexes (2016) Physiol. Meas., 37, pp. 276-290; Goldberger, A.L., Non-linear dynamics for clinicians: Chaos theory, fractals and complexity at the bedside (1996) Lancet, 347, pp. 1312-1314; Porta, A., Causal relationships between heart period and systolic arterial pressure during graded head-up tilt (2011) Amer. J. Physiol., 300, pp. R378-R386; Soderstrom, T., Stoica, P., (1988) System Identification, , Englewood Cliffs, NJ, USA: Prentice Hall; McEliece, R.J., (2002) The Theory of Information and Coding, , Cambridge, U. K. : Cambridge Univ. Press; Porta, A., Are nonlinear model-free conditional entropy approaches for the assessment of cardiac control complexity superior to the linear model-based one (2016) IEEE Trans. Biomed. Eng.; Andrzejak, R.G., Bivariate surrogate techniques: Necessity, strengths, and caveats (2003) Phys. Rev. e, 68; Eckberg, D.L., Temporal response patterns of the human sinus node to brief carotid baroreceptor stimuli (1976) J. Physiol., 258, pp. 769-782; Baselli, G., Model for the assessment of heart period and arterial pressure variability interactions and respiratory influences (1994) Med. Biol. Eng. Comput., 32, pp. 143-152; Porta, A., Accounting for respiration is necessary to reliably infer Granger causality from cardiovascular variability series (2012) IEEE Trans. Biomed. Eng., 59 (3), pp. 832-841. , Mar; Porta, A., Model-based assessment of baroreflex and cardiopulmonary couplings during graded head-up tilt (2012) Comput. Biol. Med., 42, pp. 298-305; Baselli, G., Spectral decomposition in multichannel recordings based on multivariate parametric identification (1997) IEEE Trans. Biomed. Eng., 44 (11), pp. 1092-1101. , Nov; Akaike, H., A new look at the statistical novel identification (1974) IEEE Trans. Autom. Control, 19 (6), pp. 716-723. , Dec; Faes, L., Mutual non linear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: Comparison among different strategies based on k nearest neighbors (2008) Phys. Rev. e, 78; Harder, M., Bivariate measure of redundant information (2013) Phys. Rev. e, 87; Griffith, V., Intersection information based on common randomness (2014) Entropy, 16, pp. 1985-2000; Bertschinger, N., Quantifying unique information (2014) Entropy, 16, pp. 2161-2183; Xiao, X., System identification: Amulti-signal approach for probing neural cardiovascular regulation (2005) Physiol. Meas., 26, pp. R41-R71; Cooke, W.H., Human responses to upright tilt: A window on central autonomic integration (1999) J. Physiol., 517, pp. 617-628; Montano, N., Power spectrum analysis of heart rate variability to assess changes in sympatho-vagal balance during graded orthostatic tilt (1994) Circulation, 90, pp. 1826-1831; Porta, A., Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability (2007) Amer. J. Physiol., 293, pp. H702-H708; Marchi, A., Calibrated variability of muscle sympathetic nerve activity during graded head-up tilt in humans and its link with noradrenaline data and cardiovascular rhythms (2016) Amer. J. Physiol., 310, pp. R1134-R1143; Furlan, R., Oscillatory patterns in sympathetic neural discharge and cardiovascular variables during orthostatic stimulus (2000) Circulation, 101, pp. 886-892; Faes, L., Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy (2013) Auton. Neurosci., Basic Clin., 178, pp. 76-82; Heart rate variability-Standards of measurement, physiological interpretation and clinical use (1996) Circulation, 93, pp. 1043-1065. , Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology; Porta, A., Short-term complexity indexes of heart period and systolic arterial pressure variabilities provide complementary information (2012) J. Appl. Physiol., 113, pp. 1810-1820; Saul, J.P., Transfer function analysis of the circulation: Unique insights into cardiovascular regulation (1991) Amer. J. Physiol., 261, pp. H1231-H1245; Mullen, T.J., System identification of closed loop cardiovascular control: Effects of posture and autonomic blockade (1997) Amer. J. Physiol., 272, pp. H448-H461; Nikias, L., Raghuveer, M.R., Bispectrum estimation: A digital signal processing framework (1987) Proc. IEEE, 75 (7), pp. 869-891. , Jul; Nakamura, T., Multiscale analysis of intensive longitudinal biomedical signals and its clinical applications (2016) Proc. IEEE, 104 (2), pp. 242-261. , Feb; Peng, C.-K., Long-range anticorrelations and non-Gaussian behavior of the heartbeat (1993) Phys. Rev. Lett., 70, pp. 1343-1346; Porta, A., Faes, L., Wiener-Granger causality in network physiology with applications to cardiovascular control and neuroscience (2016) Proc. IEEE, 104 (2), pp. 282-309. , Feb; Timme, N., Synergy, redundancy, andmultivariate informationmeasures: An experimentalist's perspective (2014) J. Comput. Neurosci., 36, pp. 119-140; Papana, A., Simulation study of direct causality measures in multivariate time series (2013) Entropy, 15, pp. 2635-2661; Faes, L., Linear and nonlinear analysis of brain-heart and brain-brain interactions during sleep (2015) Phys. Meas., 36, pp. 683-698; Voss, A., The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death (1996) Cardiovasc. Res., 31, pp. 419-433; Wessel, N., Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates (2000) Phys. Rev. e, 61, pp. 733-739; Barrett, A.B., Multivariate Granger causality and generalized variance (2010) Phys. Rev. e, 81; Muller, A., Causality in physiological signals (2016) Physiol. Meas., 37, pp. R46-R72

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Autonomic nervous system

KW - cardiovascular control

KW - head-down tilt (HDT)

KW - head-up tilt (HUT)

KW - heart rate variability

KW - Wiener-Granger causality

KW - Entropy

KW - Cardiovascular control

KW - Granger Causality

KW - Head-up tilts

KW - Heart rate variability

KW - Redundancy

KW - adult

KW - aged

KW - arterial pressure

KW - Article

KW - autonomic nervous system

KW - breathing

KW - cardiovascular parameters

KW - decomposition

KW - entropy

KW - extrasystole

KW - female

KW - head-down tilt

KW - heart cycle

KW - human

KW - kernel method

KW - limit of quantitation

KW - male

KW - net redundancy

KW - normal human

KW - pressoreceptor reflex

KW - prevalence

KW - QRS complex

KW - redundancy analysis

KW - systolic arterial pressure

KW - thorax pressure

U2 - 10.1109/TBME.2017.2654509

DO - 10.1109/TBME.2017.2654509

M3 - Article

VL - 64

SP - 2628

EP - 2638

JO - IEEE Transactions on Biomedical Engineering

JF - IEEE Transactions on Biomedical Engineering

SN - 0018-9294

IS - 11

ER -