# Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Protocol

#### 2.2. Time Series Extraction

_{n}); the SBP was taken as the maximum value of the arterial blood pressure inside the n-th RR interval and was denoted as SBP

_{n}; and the respiration volume signal (RESP

_{n}) was sampled at the onset of the first R-wave peak delimiting RR

_{n}. For each subject, sequences of N=300 values were extracted from the original recordings for data analysis for each phase of the protocol separately (see Figure 1). To avoid transient changes, the sequence of 300 beats for supine rest phase started 8 min after the beginning of the supine rest phase, for HUT 3 min after the change of the position, for supine recovery 7 min before starting the MA task and for MA 2 min after starting of the MA task. During the whole protocol the respiration frequency for each volunteer was > 0.15 Hz.

#### 2.3. Multiscale Information Decomposition

#### 2.4. Data Analysis and Interpretation

#### 2.5. Statistical Analysis

## 3. Results

_{SBP→RR}was observed also during MA over the last six scales (from 7 to 12, p ≤ 0.042). Moving from rest to HUT, the unique TE from RESP to RR decreased significantly at scale 1 (p < 0.001) and increased significantly at scales 3–6 (p ≤ 0.019) and 10–12 (p ≤ 0.048); during MA significantly lower values were found only at scale 1 (p = 0.031) (Figure 3d). The redundant TE from RESP, SBP to RR was higher at low scales (from 1 to 4, p < 0.001) and intermediate scales (from 5 to 7, p ≤ 0.014); during MA the significantly lower values were reached at scales 2, 8, and 9 (p ≤ 0.022) (Figure 3d). Finally, the synergistic TE was significantly higher during HUT almost across all time scales (from 1 to 9, p ≤ 0.008), while during MA no significant changes were found (0.949 ≥ p ≥ 0.141) (Figure 3f).

_{1}= 1) from effects due to slower oscillations only (VLF and LF band), we calculated the time scale individually for each recording corresponding to slower oscillations (τ

_{2}). The time scale τ

_{2}was calculated using Equation (9) and rounded to the smallest possible integer value that was greater than or equal to the given number. The median values across subjects obtained for τ

_{2}in the four phases of the experimental protocol were τ

_{2}= 4 (range: 3–5) during supine rest, τ

_{2}= 5 (range: 4–7) during HUT, τ

_{2}= 4 (range: 3–6) during supine recovery, and τ

_{2}= 5 (range: 3–7) during MA. In the following, results are presented with reference to Figure 4 showing each information measure separately for the time scales τ

_{1}and τ

_{2}.

## 4. Discussion

#### 4.1. Partial Information Decomposition of Cardiovascular and Cardiorespiratory Interactions During Postural and Mental Stress—Raw Data Analysis

#### 4.2. Multiscale Information Decomposition of Cardiovascular and Cardiorespiratory Interactions—Focus on Slower Oscillations

_{1}and τ

_{2}in the scale-specific analysis (Figure 4c). We suggest that this result arises from the fact that SBP has the most relevant part of its dynamics in the LF and VLF bands, and therefore it may transfer more information to RR when assessed only for slower oscilations. This indicates that the baroreflex is an important mechanism for slower heart rate oscillations, and supports previous studies stressing the necessity to analyse the baroreflex in the LF band and evidencing that the interpretation of baroreflex coupling and gain can be less reliable when other mechanisms (e.g., nonbaroreflex mechanisms of RSA) are involved in the genesis of RR oscillations [43].

_{2}individually for each subject; Figure 4c,d). Therefore, further studies are needed, probably considering longer time series, to support the consistency of these complex interaction patterns observed when only VLF and LF oscillations are analysed.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

**Table A1.**Results of the statistical comparison of a given measure across conditions (supine rest, HUT, supine recovery, MA) using the nonparametric Friedman test, followed by post hoc pairwise comparisons (supine rest vs. HUT; supine recovery vs. MA), and effect size calculated as Kendall’s W.

τ_{1} | τ_{2} | |||||||
---|---|---|---|---|---|---|---|---|

Supine Rest vs. HUT | Supine Recovery vs. MA | Supine Rest vs. HUT | Supine Recovery vs. MA | |||||

p-Value | Kendall’s W | p-Value | Kendall’s W | p-Value | Kendall’s W | p-Value | Kendall’s W | |

T_{RESP,SBP→RR} | <0.001 | 0.286 | 0.771 | 0.286 | <0.001 | 0.167 | 0.019 | 0.167 |

I_{RESP,SBP→RR} | <0.001 | 0.319 | 1.000 | 0.319 | 0.095 | 0.017 | 0.664 | 0.017 |

U_{SBP→RR} | <0.001 | 0.200 | 0,002 | 0.200 | 0.895 | 0.014 | 0.129 | 0.014 |

U_{RESP→RR} | <0.001 | 0.167 | 0.031 | 0.167 | 0.461 | 0.007 | 0.870 | 0.007 |

R_{RESP,SBP→RR} | <0.001 | 0.420 | 0.107 | 0.420 | 0.017 | 0.058 | 0.612 | 0.058 |

S_{RESP,SBP→RR} | 0.003 | 0.043 | 0.660 | 0.043 | <0.001 | 0.106 | 0.696 | 0.106 |

**Table A2.**Results of the statistical comparison between each information measure computed at scales τ

_{1}and τ

_{2}using the Wilcoxon signed-rank test, and corresponding effect size expressed as Kendall’s W.

Supine Rest | HUT | Supine Recovery | MA | |||||
---|---|---|---|---|---|---|---|---|

p-Value | Kendall’s W | p-Value | Kendall’s W | p-Value | Kendall’s W | p-Value | Kendall’s W | |

T_{RESP,SBP→RR} | <0.001 | 0.760 | <0.001 | 0.805 | <0.001 | 0.852 | <0.001 | 0.900 |

I_{RESP,SBP→RR} | 0.001 | 0.148 | <0.001 | 0.716 | 0.006 | 0.080 | 0.010 | 0.111 |

U_{SBP→RR} | <0.001 | 0.331 | 0.321 | 0.001 | <0.001 | 0.319 | 0.964 | 0.021 |

U_{RESP→RR} | <0.001 | 0.562 | 0.174 | 0.055 | <0.001 | 0.486 | <0.001 | 0.216 |

R_{RESP,SBP→RR} | <0.001 | 0.632 | <0.001 | 0.949 | <0.001 | 0.673 | <0.001 | 0.760 |

S_{RESP,SBP→RR} | <0.001 | 0.805 | <0.001 | 0.592 | <0.001 | 0.900 | <0.001 | 0.760 |

## References

- Shaffer, F.; Ginsberg, J.P. An Overview of Heart Rate Variability Metrics and Norms. Front. Public Health
**2017**, 5, 258. [Google Scholar] [CrossRef] [PubMed] - Shaffer, F.; McCraty, R.; Zerr, C.L. A healthy heart is not a metronome: an integrative review of the heart’s anatomy and heart rate variability. Front. Psychol.
**2014**, 5, 1040. [Google Scholar] [CrossRef] [PubMed] - Voss, A.; Schulz, S.; Schroeder, R.; Baumert, M.; Caminal, P. Methods derived from nonlinear dynamics for analysing heart rate variability. Philos. Trans. Ser. A, Math., Phys., Eng. Sci.
**2009**, 367, 277–296. [Google Scholar] [CrossRef] - McCraty, R.; Atkinson, M.; Tomasino, D.; Bradley, R.T. The Coherent Heart: Heart-brain Interactions, Psychophysiological Coherence, and the Emergence of System-wide Order; HearthMath Research Center, Institute of HeartMath: Boulder Creek, CA, USA, 2006. [Google Scholar]
- Schumann, A.; Schulz, S.; Voss, A.; Scharbrodt, S.; Baumert, M.; Bar, K.J. Baroreflex Coupling Assessed by Cross-Compression Entropy. Front. Phys.
**2017**, 8, 282. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cohen, M.A.; Taylor, J.A. Short-term cardiovascular oscillations in man: measuring and modelling the physiologies. J. Phys.
**2002**, 542, 669–683. [Google Scholar] [CrossRef] - Katona, P.G.; Poitras, J.W.; Barnett, G.O.; Terry, B.S. Cardiac vagal efferent activity and heart period in the carotid sinus reflex. Am. J. Phys.
**1970**, 218, 1030–1037. [Google Scholar] [CrossRef] [Green Version] - Heart rate variability: standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Circulation
**1996**, 93, 1043–1065. [CrossRef] - Voss, A.; Kurths, J.; Kleiner, H.J.; Witt, A.; Wessel, N. Improved analysis of heart rate variability by methods of nonlinear dynamics. J. Electrocardiol.
**1995**, 28, 81–88. [Google Scholar] [CrossRef] - Dick, T.E.; Hsieh, Y.H.; Dhingra, R.R.; Baekey, D.M.; Galan, R.F.; Wehrwein, E.; Morris, K.F. Cardiorespiratory coupling: common rhythms in cardiac, sympathetic, and respiratory activities. Prog. Brain Res.
**2014**, 209, 191–205. [Google Scholar] [CrossRef] - Bar, K.J.; Schuhmacher, A.; Hofels, S.; Schulz, S.; Voss, A.; Yeragani, V.K.; Maier, W.; Zobel, A. Reduced cardio-respiratory coupling after treatment with nortriptyline in contrast to S-citalopram. J. Affect. Disord.
**2010**, 127, 266–273. [Google Scholar] [CrossRef] - Marwan, N.; Zou, Y.; Wessel, N.; Riedl, M.; Kurths, J. Estimating coupling directions in the cardiorespiratory system using recurrence properties. Philos. Trans. Ser. A, Math., Phys., Eng. Sci.
**2013**, 371, 20110624. [Google Scholar] [CrossRef] [Green Version] - Peupelmann, J.; Quick, C.; Berger, S.; Hocke, M.; Tancer, M.E.; Yeragani, V.K.; Bar, K.J. Linear and non-linear measures indicate gastric dysmotility in patients suffering from acute schizophrenia. Prog. Neuro-Psychopharmacol. Biol. Psychiatry
**2009**, 33, 1236–1240. [Google Scholar] [CrossRef] - Penzel, T.; Porta, A.; Stefanovska, A.; Wessel, N. Recent advances in physiological oscillations. Physiol. Meas.
**2017**, 38, E1–E7. [Google Scholar] [CrossRef] - Nollo, G.; Faes, L.; Porta, A.; Antolini, R.; Ravelli, F. 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.
**2005**, 288, 1777–1785. [Google Scholar] [CrossRef] - Silvani, A.; Calandra-Buonaura, G.; Johnson, B.D.; Van Helmond, N.; Barletta, G.; Cecere, A.G.; Joyner, M.J.; Cortelli, P. Physiological Mechanisms Mediating the Coupling between Heart Period and Arterial Pressure in Response to Postural Changes in Humans. Front. Physiol.
**2017**, 8, 163. [Google Scholar] [CrossRef] [PubMed] - Faes, L.; Nollo, G.; Porta, A. Mechanisms of causal interaction between short-term RR interval and systolic arterial pressure oscillations during orthostatic challenge. J. Appl. Physiol.
**2013**, 114, 1657–1667. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Nollo, G.; Faes, L.; Porta, A.; Pellegrini, B.; Ravelli, F.; Del Greco, M.; Disertori, M.; Antolini, R. Evidence of unbalanced regulatory mechanism of heart rate and systolic pressure after acute myocardial infarction. Am. J. Physiol. Heart Circ. Physiol.
**2002**, 283, 1200–1207. [Google Scholar] [CrossRef] - Porta, A.; Furlan, R.; Rimoldi, O.; Pagani, M.; Malliani, A.; Van De Borne, P. Quantifying the strength of the linear causal coupling in closed loop interacting cardiovascular variability signals. Biol. Cybern.
**2002**, 86, 241–251. [Google Scholar] [CrossRef] - Lenis, G.; Kircher, M.; Lázaro, J.; Bailón, R.; Gil, E.; Doessel, O. Separating the effect of respiration on the heart rate variability using Granger’s causality and linear filtering. Biomed. Signal Process. Control
**2017**, 31, 272–287. [Google Scholar] [CrossRef] - Porta, A.; Baselli, G.; Lombardi, F.; Montano, N.; Malliani, A.; Cerutti, S. Conditional entropy approach for the evaluation of the coupling strength. Biol. Cybern.
**1999**, 81, 119–129. [Google Scholar] [CrossRef] [PubMed] - Faes, L.; Nollo, G.; Porta, A. Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique. Phys. Rev. E, Stat., Nonlinear, Soft Matter Phys.
**2011**, 83, 051112. [Google Scholar] [CrossRef] [Green Version] - Faes, L.; Nollo, G.; Porta, A. Information domain approach to the investigation of cardio-vascular, cardio-pulmonary, and vasculo-pulmonary causal couplings. Front. Phys.
**2011**, 2, 80. [Google Scholar] [CrossRef] - Faes, L.; Porta, A.; Cucino, R.; Cerutti, S.; Antolini, R.; Nollo, G. Causal transfer function analysis to describe closed loop interactions between cardiovascular and cardiorespiratory variability signals. Biol. Cybern.
**2004**, 90, 390–399. [Google Scholar] [CrossRef] [PubMed] - Porta, A.; Bassani, T.; Bari, V.; Tobaldini, E.; Takahashi, A.C.; Catai, A.M.; Montano, N. Model-based assessment of baroreflex and cardiopulmonary couplings during graded head-up tilt. Comput. Biol. Med.
**2012**, 42, 298–305. [Google Scholar] [CrossRef] - Javorka, M.; Krohova, J.; Czippelova, B.; Turianikova, Z.; Lazarova, Z.; Javorka, K.; Faes, L. Basic cardiovascular variability signals: mutual directed interactions explored in the information domain. Physiol. Meas.
**2017**, 38, 877–894. [Google Scholar] [CrossRef] [PubMed] - Faes, L.; Nollo, G.; Porta, A. Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series. Comput. Biol. Med.
**2012**, 42, 290–297. [Google Scholar] [CrossRef] [PubMed] - Faes, L.; Porta, A.; Nollo, G.; Javorka, M. Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks. Entropy
**2017**, 19, 5. [Google Scholar] [CrossRef] - Faes, L.; Marinazzo, D.; Stramaglia, S. Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes. Entropy
**2017**, 19, 408. [Google Scholar] [CrossRef] - Faes, L.; Bari, V.; Ranucci, M.; Porta, A. Multiscale Decomposition of Cardiovascular and Cardiorespiratory Information Transfer under General Anesthesia. In Proceedings of the 40th International Conference of the IEEE Engineering in Medicine and Biology Society, Honolulu, HI USA, 17–21 July 2018; pp. 4607–4610. [Google Scholar] [CrossRef]
- Javorka, M.; Krohova, J.; Czippelova, B.; Turianikova, Z.; Lazarova, Z.; Wiszt, R.; Faes, L. Towards understanding the complexity of cardiovascular oscillations: Insights from information theory. Comput. Biol. Med.
**2018**, 98, 48–57. [Google Scholar] [CrossRef] - Williams, P.L.; Beer, R.D. Nonnegative Decomposition of Multivariate Information. arXiv
**2010**, arXiv:1004.2515. [Google Scholar] - Timme, N.; Alford, W.; Flecker, B.; Beggs, J.M. Synergy, redundancy, and multivariate information measures: an experimentalist’s perspective. J. Comput. Neurosci.
**2014**, 36, 119–140. [Google Scholar] [CrossRef] - Barrett, A.B. Exploration of synergistic and redundant information sharing in static and dynamical Gaussian systems. Phys. Rev. E, Stat., Nonlinear, Soft Matter Phys.
**2015**, 91, 052802. [Google Scholar] [CrossRef] [Green Version] - Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control
**1974**, 19, 716–723. [Google Scholar] [CrossRef] - Badra, L.J.; Cooke, W.H.; Hoag, J.B.; Crossman, A.A.; Kuusela, T.A.; Tahvanainen, K.U.; Eckberg, D.L. Respiratory modulation of human autonomic rhythms. Am. J. Phys. Heart Circ. Physiol.
**2001**, 280, 2674–2688. [Google Scholar] [CrossRef] [PubMed] - Eckberg, D.L. Point:counterpoint: respiratory sinus arrhythmia is due to a central mechanism vs. respiratory sinus arrhythmia is due to the baroreflex mechanism. J. Appl. Physiol.
**2009**, 106. [Google Scholar] [CrossRef] [PubMed] - Koepchen, H.P.; Klussendorf, D.; Sommer, D. Neurophysiological background of central neural cardiovascular-respiratory coordination: basic remarks and experimental approach. J. Auton. Nerv. Syst.
**1981**, 3, 335–368. [Google Scholar] [CrossRef] - Porta, A.; Bari, V.; De Maria, B.; Takahashi, A.C.M.; Guzzetti, S.; Colombo, R.; Catai, A.M.; Raimondi, F.; Faes, L. Quantifying Net Synergy/Redundancy of Spontaneous Variability Regulation via Predictability and Transfer Entropy Decomposition Frameworks. IEEE Trans. Bio-Med. Eng.
**2017**, 64, 2628–2638. [Google Scholar] [CrossRef] - Karemaker, J.M. Counterpoint: respiratory sinus arrhythmia is due to the baroreflex mechanism. J. Appl. Physiol.
**2009**, 106, 1742–1743, discussion 1744. [Google Scholar] [CrossRef] [PubMed] - Krohova, J.; Czippelova, B.; Turianikova, Z.; Lazarova, Z.; Wiszt, R.; Javorka, M.; Faes, L. Information domain analysis of respiratory sinus arrhythmia mechanisms. Physiol. Res.
**2018**, 67, 611–618. [Google Scholar] [CrossRef] - Hirsch, J.A.; Bishop, B. Respiratory sinus arrhythmia in humans: how breathing pattern modulates heart rate. Am. J. Physiol.
**1981**, 241, 620–629. [Google Scholar] [CrossRef] [PubMed] - Porta, A.; Baselli, G.; Rimoldi, O.; Malliani, A.; Pagani, M. Assessing baroreflex gain from spontaneous variability in conscious dogs: role of causality and respiration. Am. J. Physiol. Heart Circ. Physiol.
**2000**, 279, 2558–2567. [Google Scholar] [CrossRef] [PubMed] - Milde, T.; Schwab, K.; Walther, M.; Eiselt, M.; Schelenz, C.; Voss, A.; Witte, H. Time-variant partial directed coherence in analysis of the cardiovascular system. A methodological study. Physiol. Meas.
**2011**, 32, 1787–1805. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Timeline of the study protocol with indication of the timing of the sequences of 300 beats selected for the analysis.

**Figure 2.**Information decomposition of cardiovascular and cardiorespiratory interactions. (

**a**) Interaction information decomposition diagram depicting how the joint TE from respiration pattern (RESP) and systolic blood pressure (SBP) to RR is expanded as the sum of the two individual TEs from RESP to RR (violet) and from SBP to RR (yellow), plus the interaction TE from RESP and SBP to RR (orange); (

**b**) Partial Information decomposition diagram showing how the joint TE from RESP and SBP to RR is expanded as the sum of the two unique TEs from RESP to RR (blue) and from SBP to RR (green), plus the redundant TE (red) and the synergistic TE (light blue) from RESP and SBP to RR; (

**c**) Causal interaction diagram depicting the direct effects of RESP on RR (blue arrow), the effects of RESP on SBP (red arrow) and the effects of SBP on RR (green arrow).

**Figure 3.**Multiscale information decomposition during the four phases of the experimental protocol (supine rest, HUT; supine recovery, MA). Plots represent the distributions (median and interquartile range) of (

**a**) the joint TE (T

_{RESP,SBP→RR}), (

**b**) the interaction TE (I

_{RESP,SBP→RR}), (

**c**) the unique TE from SBP to RR (U

_{SBP}

_{→}

_{RR}) and (

**d**) from RESP to RR (U

_{RESP→RR}), (

**e**) the redundant TE (R

_{RESP,SBP→RR}) and (

**f**) the synergistic TE (S

_{RESP,SBP→RR}), computed as a function of the time scale τ. # denotes statistically significant difference between the first and second phase (an effect of HUT) and * denotes statistically significant difference between the third and fourth phase (an effect of MA).

**Figure 4.**Multiscale information decomposition during the four phases of the experimental protocol (supine rest, HUT; supine recovery, MA) calculated for the scales representing raw data (τ

_{1}= 1) and slower oscillations only (τ

_{2}). Plots depict the distributions (box plots and individual values) of (

**a**) the joint TE (T

_{RESP,SBP→RR}), (

**b**) the interaction TE (I

_{RESP,SBP→RR}), (

**c**) the unique TE from SBP to RR (U

_{SBP→RR}), (

**d**) the unique TE from RESP to RR (U

_{RESP→RR}), (

**e**) the redundant TE (R

_{RESP,SBP→RR}) and (

**f**) the synergistic TE (S

_{RESP,SBP→RR}). # Denotes statistically significant difference between the first and second phase (supine rest vs. HUT), *denotes statistically significant difference between the third and fourth phase (supine recovery vs. MA), and $ denotes statistically significant difference between raw data (τ

_{1}) and slower oscillations (τ

_{2}) during the same phase.

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## Share and Cite

**MDPI and ACS Style**

Krohova, J.; Faes, L.; Czippelova, B.; Turianikova, Z.; Mazgutova, N.; Pernice, R.; Busacca, A.; Marinazzo, D.; Stramaglia, S.; Javorka, M.
Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress. *Entropy* **2019**, *21*, 526.
https://doi.org/10.3390/e21050526

**AMA Style**

Krohova J, Faes L, Czippelova B, Turianikova Z, Mazgutova N, Pernice R, Busacca A, Marinazzo D, Stramaglia S, Javorka M.
Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress. *Entropy*. 2019; 21(5):526.
https://doi.org/10.3390/e21050526

**Chicago/Turabian Style**

Krohova, Jana, Luca Faes, Barbora Czippelova, Zuzana Turianikova, Nikoleta Mazgutova, Riccardo Pernice, Alessandro Busacca, Daniele Marinazzo, Sebastiano Stramaglia, and Michal Javorka.
2019. "Multiscale Information Decomposition Dissects Control Mechanisms of Heart Rate Variability at Rest and During Physiological Stress" *Entropy* 21, no. 5: 526.
https://doi.org/10.3390/e21050526