Medical & Biological Engineering & Computing

, Volume 55, Issue 2, pp 179–190 | Cite as

Causal analysis of short-term cardiovascular variability: state-dependent contribution of feedback and feedforward mechanisms

  • Michal JavorkaEmail author
  • Barbora Czippelova
  • Zuzana Turianikova
  • Zuzana Lazarova
  • Ingrid Tonhajzerova
  • Luca Faes
Original Article


Baroreflex function is usually assessed from spontaneous oscillations of blood pressure (BP) and cardiac RR interval assuming a unidirectional influence from BP to RR. However, the interaction of BP and RR is bidirectional—RR also influences BP. Novel methods based on the concept of Granger causality were recently developed for separate analysis of feedback (baroreflex) and feedforward (mechanical) interactions between RR and BP. We aimed at assessing the proportion of the two causal directions of the interactions between RR and systolic BP (SBP) oscillations during various conditions, and at comparing causality measures from SBP to RR with baroreflex gain indexes. Arterial BP and ECG signals were noninvasively recorded in 16 young healthy volunteers during supine rest, mental arithmetics, and head-up tilt test, as well as during the combined administration of these stressors. The causal interactions between beat-to-beat RR and SBP signals were analyzed in time, frequency, and information domains. The baroreflex gain was assessed in the frequency domain using non-causal and causal measures of the transfer function from SBP to RR. We found a consistent increase in the baroreflex coupling strength from SBP to RR during head-up tilt, an insensitivity of the coupling strength along the non-baroreflex direction to both stressors, and no significant effect of mental arithmetics on the feedback coupling strength. It indicates that the proportion of causal interactions between SBP and RR significantly varies during different conditions. The increase in the coupling from SBP to RR with tilt was not accompanied by concomitant variations of the transfer function gain, suggesting that causality and gain analyses are complementary and assess different aspects of the baroreflex regulation of heart rate.


Baroreflex Head-up tilt Mental arithmetics Granger causality Information domain 



The study was supported by grants APVV-0235-12, VEGA 1/0059/13 and project “Biomedical Center Martin,” ITMS code: 26220220187, and the project is co-financed from EU sources. Luca Faes was supported by the Healthcare Research Implementation Program (IRCS), Provincia Autonoma di Trento and Bruno Kessler Foundation, Italy.


  1. 1.
    Aletti F, Bassani T, Lucini D et al (2009) Multivariate decomposition of arterial blood pressure variability for the assessment of arterial control of circulation. IEEE Trans Biomed Eng 56(7):1781–1790CrossRefPubMedGoogle Scholar
  2. 2.
    Barbieri R, Parati G, Saul JP (2001) Closed-versus open-loop assessment of heart rate baroreflex. IEEE Eng Med Biol Mag 20(2):33–42CrossRefPubMedGoogle Scholar
  3. 3.
    Baselli G, Cerutti S, Civardi S et al (1988) Cardiovascular variability signals: towards the identification of a closed-loop model of the neural control mechanisms. IEEE Trans Biomed Eng 35(12):1033–1046CrossRefPubMedGoogle Scholar
  4. 4.
    Baselli G, Cerutti S, Livraghi M et al (1988) Causal relationship between heart rate and arterial blood pressure variability signals. Med Biol Eng Comput 26(4):374–378CrossRefPubMedGoogle Scholar
  5. 5.
    Baselli G, Cerutti S, Badilini F et al (1994) Model for the assessment of heart period and arterial pressure variability interactions and of respiration influences. Med Biol Eng Comput 32(2):143–152CrossRefPubMedGoogle Scholar
  6. 6.
    Berntson GG, Cacioppo JT, Binkley PF, Uchino BN, Quigley KS, Fieldstone A (1994) Autonomic cardiac control. III. Psychological stress and cardiac response in autonomic space as revealed by pharmacological blockades. Psychophysiology 31(6):599–608CrossRefPubMedGoogle Scholar
  7. 7.
    Eckberg DL, Sleight P (1992) Human baroreflexes in health and disease. Clarendon Press, OxfordGoogle Scholar
  8. 8.
    Faes L, Erla S, Nollo G (2012) Measuring connectivity in linear multivariate processes: definitions, interpretation, and practical analysis. Comput Math Methods Med 2012 Article ID 140513. doi: 10.1155/2012/140513
  9. 9.
    Faes L, Marinazzo D, Montalto A, Nollo G (2014) Lag-specific transfer entropy as a tool to assess cardiovascular and cardiorespiratory information transfer. IEEE Trans Biomed Eng 61(10):2556–2568. doi: 10.1109/TBME.2014.2323131 CrossRefPubMedGoogle Scholar
  10. 10.
    Faes L, Mase M, Nollo G, Chon KH, Florian JP (2013) Measuring postural-related changes of spontaneous baroreflex sensitivity after repeated long-duration diving: frequency domain approaches. Auton Neurosci 178(1–2):96–102. doi: 10.1016/j.autneu.2013.03.006 CrossRefPubMedGoogle Scholar
  11. 11.
    Faes L, Nollo G, Chon KH (2008) Assessment of Granger causality by nonlinear model identification: application to short-term cardiovascular variability. Ann Biomed Eng 36(3):381–395. doi: 10.1007/s10439-008-9441-z CrossRefPubMedGoogle Scholar
  12. 12.
    Faes L, Nollo G, Porta A (2011) Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings. Front Physiol 2:80. doi: 10.3389/fphys.2011.00080 CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Faes L, Nollo G, Porta A (2012) Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series. Comput Biol Med 42:290–297. doi: 10.1016/j.compbiomed.2011.02.007 CrossRefPubMedGoogle Scholar
  14. 14.
    Faes L, Nollo G, Porta A (2013) Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge. J Appl Physiol 114(12):1657–1667. doi: 10.1152/japplphysiol.01172.2012 CrossRefPubMedGoogle Scholar
  15. 15.
    Faes L, Porta A (2014) Conditional entropy-based evaluation of information dynamics in physiological systems. In: Vicente R, Wibral M, Lizier JT (eds) Directed information measures in neuroscience. Springer, Berlin, pp 61–86CrossRefGoogle Scholar
  16. 16.
    Granger CWJ (1963) Economic processes involving feedback. Inf Control 6:28–48CrossRefGoogle Scholar
  17. 17.
    Julien C (2006) The enigma of Mayer waves: facts and models. Cardiovasc Res 70(1):12–21CrossRefPubMedGoogle Scholar
  18. 18.
    Kuipers NT, Sauder CL, Carter JR, Ray CA (2008) Neurovascular responses to mental stress in the supine and upright postures. J Appl Physiol 104:1129–1136. doi: 10.1152/japplphysiol.01285.2007 CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    La Rovere MT, Pinna GD, Maestri R, Sleight P (2013) Clinical value of baroreflex sensitivity. Neth Heart J 21:61–63. doi: 10.1007/s12471-012-0349-8 CrossRefPubMedGoogle Scholar
  20. 20.
    Lackner KL, Papousek I, Batzel JJ, Roessler A, Scharfetter H, Hinghofer-Szalkay H (2011) Phase synchronization of hemodynamic variables and respiration during mental challenge. Int J Psychophysiol 79:401–409. doi: 10.1016/j.ijpsycho.2011.01.001 CrossRefPubMedGoogle Scholar
  21. 21.
    Ljung L (1987) System identification: theory for the user. Prentice Hall, Englewood CliffsGoogle Scholar
  22. 22.
    Lucini D, Porta A, Milani O et al (2000) Assessment of arterial and cardiopulmonary baroreflex gains from simultaneous recordings of spontaneous cardiovascular and respiratory variability. J Hypertens 18(3):281–286CrossRefPubMedGoogle Scholar
  23. 23.
    Lutkepohl H (1993) Introduction to multiple time series analysis. Springer, BerlinCrossRefGoogle Scholar
  24. 24.
    Melillo P, Bracale M, Pecchia L (2011) Nonlinear Heart Rate Variability features for real-life stress detection. Case study: students under stress due to university examination. Biomed Eng Online 10:96CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Mullen TJ, Appel ML, Mukkamala R et al (1997) System identification of closed loop cardiovascular control: effects of posture and autonomic blockade. Am J Physiol 272(1 Pt 2):H448–H461PubMedGoogle Scholar
  26. 26.
    Nollo G, Faes L, Porta A, Antolini R, Ravelli F (2005) Exploring directionality in spontaneous heart period and systolic pressure variability interactions in humans: implications in the evaluation of baroreflex gain. Am J Physiol Heart Circ Physiol 288:H1777–H1785CrossRefPubMedGoogle Scholar
  27. 27.
    Paton JF, Boscan P, Pickering AE, Nalivaiko E (2005) The yin and yang of cardiovascular autonomic control: vago-sympathetic interactions revisited. Brain Res Rev 49:555–565CrossRefPubMedGoogle Scholar
  28. 28.
    Pinna GD, Maestri R (2002) New criteria for estimating baroreflex sensitivity using the transfer function method. Med Biol Eng Comput 40(1):79–84CrossRefPubMedGoogle Scholar
  29. 29.
    Pinna GD, Maestri R, Raczak G et al (2002) Measuring baroreflex sensitivity from the gain function between arterial pressure and heart period. Clin Sci (Lond) 103(1):81–88CrossRefGoogle Scholar
  30. 30.
    Porta A, Baselli G, Rimoldi O et al (2000) Assessing baroreflex gain from spontaneous variability in conscious dogs: role of causality and respiration. Am J Physiol 279(5):H2558–H2567Google Scholar
  31. 31.
    Porta A, Bassani T, Bari V, Pinna GD, Maestri R, Guzzetti S (2012) Accounting for respiration is necessary to reliably infer granger causality from cardiovascular variability series. IEEE T Biomed Eng 59:832–841. doi: 10.1109/TBME.2011.2180379 CrossRefGoogle Scholar
  32. 32.
    Porta A, Furlan R, Rimoldi O, Pagani M, Malliani A, van de Borne P (2002) Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals. Biol Cybern 86:241–251CrossRefPubMedGoogle Scholar
  33. 33.
    Porta A, Faes L (2013) Assessing causality in brain dynamics and cardiovascular control. Philos Trans R Soc A Math Phys Eng Sci 371(1997):20120517CrossRefGoogle Scholar
  34. 34.
    Porta A, Faes L (2016) Wiener-Granger causality in network physiology with applications to cardiovascular control and neuroscience. Proc IEEE 104(2):282–309CrossRefGoogle Scholar
  35. 35.
    Robbe HWJ, Mulder LJM, Ruddel H et al (1987) Assessment of baroreceptor reflex sensitivity by means of spectral analysis. Hypertension 10:538–543CrossRefPubMedGoogle Scholar
  36. 36.
    Saperova E, Dimitriev D (2015) Heart rate variability as a measure of autonomic regulation of cardiac activity during mental stress. FASEB J. doi: 10.1096/fj.1530-6860 Google Scholar
  37. 37.
    Schulz S, Adochiei FC, Edu IR et al (2013) Cardiovascular and cardiorespiratory coupling analyses: a review. Philos Trans R Soc A 371(1997):20120191CrossRefGoogle Scholar
  38. 38.
    Taylor JA, Eckberg DL (1996) Fundamental relations between short-term RR interval and arterial pressure oscillations in humans. Circulation 93:1527–1532CrossRefPubMedGoogle Scholar
  39. 39.
    Toska K, Eriksen M (1993) Respiration-synchronous fluctuations in stroke volume, heart rate and arterial pressure in humans. J Physiol 472:501–512CrossRefPubMedPubMedCentralGoogle Scholar
  40. 40.
    Triedman JK, Saul JP (1994) Blood pressure modulation by central venous pressure and respiration. Buffering effects of the heart rate reflexes. Circulation 89:169–179CrossRefPubMedGoogle Scholar
  41. 41.
    Widjaja D, Montalto A, Vlemincx E, Marinazzo D, Van Huffel S, Faes L (2015) Cardiorespiratory information dynamics during mental arithmetic and sustained attention. PLoS One 10(6):e0129112. doi: 10.1371/journal.pone.0129112 CrossRefPubMedPubMedCentralGoogle Scholar
  42. 42.
    Wiener N (1956) The theory of prediction. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2016

Authors and Affiliations

  • Michal Javorka
    • 1
    • 2
    Email author
  • Barbora Czippelova
    • 2
  • Zuzana Turianikova
    • 2
  • Zuzana Lazarova
    • 1
    • 2
  • Ingrid Tonhajzerova
    • 1
    • 2
  • Luca Faes
    • 3
    • 4
  1. 1.Department of Physiology, Jessenius Faculty of MedicineComenius University in BratislavaMartinSlovakia
  2. 2.Biomedical Center Martin, Jessenius Faculty of MedicineComenius University in BratislavaMartinSlovakia
  3. 3.Healthcare Research and Innovation ProgramFBKTrentoItaly
  4. 4.BIOTech, Department of Industrial EngineeringUniversity of TrentoMattarello, TrentoItaly

Personalised recommendations