Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Analysis of generic coupling between EEG activity and PETCO2 in free breathing and breath-hold tasks using Maximal Information Coefficient (MIC)

Abstract

Brain activations related to the control of breathing are not completely known. The respiratory system is a non-linear system. However, the relationship between neural and respiratory dynamics is usually estimated through linear correlation measures, completely neglecting possible underlying nonlinear interactions. This study evaluate the linear and nonlinear coupling between electroencephalographic (EEG) signal and variations in carbon dioxide (CO2) signal related to different breathing task. During a free breathing and a voluntary breath hold tasks, the coupling between EEG power in nine different brain regions in delta (1–3 Hz) and alpha (8–13 Hz) bands and end-tidal CO2 (PET CO2) was evaluated. Specifically, the generic associations (i.e. linear and nonlinear correlations) and a “pure” nonlinear correlations were evaluated using the maximum information coefficient (MIC) and MIC-ρ2 between the two signals, respectively (where ρ2 represents the Pearson’s correlation coefficient). Our results show that in delta band, MIC indexes discriminate the two tasks in several regions, while in alpha band the same behaviour is observed for MIC-ρ2, suggesting a generic coupling between delta EEG power and PETCO2 and a pure nonlinear interaction between alpha EEG power and PETCO2. Moreover, higher indexes values were found for breath hold task respect to free breathing.

Introduction

The mechanism underlying breathing control is not totally understood at the moment. Several mathematical models have been developed to describe the control of breathing, following the hypothesis that the respiratory system could be considered as a closed loop, with a specific transit time1. In these models, the control of ventilation is described considering the relationship between the changes in carbon dioxide (CO2) and oxygen (O2) and ventilation. Some models describe the dynamics between CO2 and ventilation using a linear interaction2,3,4. However, this assumption does not consider that the respiratory system is a non-linear system5, especially moving away from the steady state, as in oscillatory phenomena, such as periodic breathing or central/obstructive apneas. For this reason, some models hypothesized a non-linear relationship between the changes in CO2 and ventilation6,7,8.

A fundamental role in the control of breathing is played by the central nervous system (CNS). It is known that the breathing control originates in the brainstem9. In these brain areas, the central chemoreceptors are sensitive to CO2 variation. Specifically, when an increase in arterial CO2 level occurs (hypercania) a subsequent increase in ventilation is observed1 to maintain homoeostatic level of gases in blood10, both in health11 and disease12. Not only the brainstem, but also cortical and subcortical areas are involved in breathing processes13,14,15,16,17. Generally, hypercapnia also causes vasodilation, and it is responsible of a certain number of vascular changes in the brain, such as variation in cerebral blood flow and cerebral blood volume18, usually following linear dynamics. On the other hand, considering the neural activity related to hypercapnia, different effects have been observed. Neuronal oscillatory power is strongly linked to arterial CO2 increase19 and both linear and non linear relationship have been hypothesized9. Another difference between the vascular and neural pattern of CO2 response is that the former is mainly widespread while the latter may be regionally heterogeneous.

The effect of hypercapnia on brain activity has been explored by gas administration using electroencephalography (EEG)20,21. Hypercapnia reduces spontaneous neuronal oscillatory power in anaesthetized primate22 and rats with intracortical electrodes23 and, if prolonged (8 weeks), causes hypnotic effects without changing the morphological aspect of the brain in rabbits24. In humans, it is responsible for increasing the δ band (1–4 Hz) EEG power as well as for decreasing the power in the α (8–13 Hz) band25,26, suggesting that during hypercapnic inhalation, brain activity resembles low arousal state. Furthermore, it has been observed a reduction in EEG power not only in α- but also in β-, and γ-frequency bands22,27.

Voluntary breath hold can be considered an alternative to gas induced hypercapnia to evaluate the relationship between CO2 and brain activity variations. Indeed, voluntary breath hold is easy to perform and has the advantage to reach arterial hypercapnia without requiring a specific device for the CO2 administration28. This kind of task allows to observe the effect of a progressive increase in arterial CO2, differently from gas administration where a step increase (square wave) to supraphysiological CO2 ranges is often achieved. Moreover, it resembles some features of the respiratory dynamics observed in obstructive sleep apnea (OSA) and central sleep apnea (CSA), where a sinusoidal increase of about 1 kPa (that correspond to about 7.5 mmHg) is usually recorded29,30 during an average apnea length around 30 seconds31,32,33. Obviously, the respiratory cycle timing is fundamental to stress the chemoreflex system in the right range of perturbation. While, past studies used too long (80–225 seconds) or too short (10 seconds) voluntary breath hold intervals34,35, a more recent study by our group explored the cross correlation between EEG global field power (GFP) in δ band and end-tidal CO2 (PETCO2) during 30 seconds of breath hold finding that the variation of PETCO2 precedes the variations of GFP36. However, in36 only a linear relationship between the two signal was considered, studying only the Pearson coefficient (ρ) at different time shifts and completely excluding non-linear interactions. Further, only the global EEG power was analysed without considering potential different responses in regional cortical areas.

To capture both linear and non-linear coupling between two variables it is possible to compute the maximal information coefficient (MIC)37. MIC was proved to be a valid index to construct the brain functional network38. It was used to highlight the non-linearity of neurovascular coupling between EEG and BOLD signals in a simultaneous EEG-fMRI study39. Moreover, MIC was used to observe the brain-heart interaction in volunteers during viewing of pictures from the International Affective Picture System (IAPS)40.

Here, we want to study the complex relationship between PETCO2 and EEG power variations, using MIC analysis. Indeed, MIC includes both linear and non-linear relationship and for this reason also MIC-ρ2 has been considered as a measure of “pure” non-linear interactions. We evaluated the effects of breath hold task locally, on nine different brain regions obtained dividing the scalp in 3 rostrocaudal sections (anterior, central, and posterior) and 3 sagittaly sections (left, middle, and right). Understanding both linear and non-linear mechanisms underlying the neuronal response to hypercapnia at regional level could be useful to disentangle the vascular and neuronal response to CO2 variations.

Results

In Figs 3 and 4 the scatter plot of the reported MIC and MIC-ρ2 values are shown for delta and alpha band, respectively. Different values of sum of squared differences were observed. Specifically, larger deviations from the bisector were observed in the BH task with respect to the FB task in the delta band. In Table 1 the distances of the scatter points from the bisector are shown. A larger number of significant differences were found in the delta band (LA, RA, MP, MC) with respect to those estimated in the alpha band (MP).

Discussion

In this study, the relationship between end tidal carbon dioxide (PETCO2) and EEG power was explored in delta and alpha bands in nine different cortical regions of eleven healthy subjects during free breathing (FB) and voluntary breath hold (BH) tasks. Specifically, we studied the generic, i.e. linear and nonlinear, interaction by means of the Maximal Information Coefficient(MIC). We found that the wider oscillations in CO2 levels obtained during BH as compared to FB were associated with a change in the delta band power widely involving the anterior and central regions of the cortex, with both linear (predominant) and nonlinear relationships between PETCO2 and EEG activity. On the other hand, during the same maneuver, the change in the alpha band was observed in a more restricted region (stronger in the middle anterior area) and was characterized by a mainly nonlinear relationship between PETCO2 and EEG activity.

The main methodological novelty of the study has been the application of MIC (a generic linear and nonlinear correlation measure) and MIC-ρ2 (a “pure” nonlinear correlation measure) indexes37. This choice was motivated by the need of introducing a more general measure of the coupling between brain and respiratory activity. In fact, brain-respiratory interactions cannot be considered purely linear, since biological function in humans involves many nonlinear oscillations and feedbacks at different system levels (as cardiac, neural, respiratory, and endocrine)41. Furthermore, we analysed the regional effect of CO2 changes to highlight the dynamics of specific areas involved by bulbo-cortical pathways. In this work, the analysis of EEG activity was limited to the delta and alpha bands, since they seem to be highly influenced by hypercapnic stimuli25,26,34,36,42,43. The estimated MIC values were found to be significant in all areas and conditions. The significance of our results could have been inferred from the tables in37 where the significance level are computed for various MIC scores at a maximum size of 760 samples. Nonetheless, surrogate data analysis was performed using the approach suggested in37.

Methods

Experimental protocol

Eleven healthy subjects (all males, age 30 ± 6) underwent the experimental protocol. EEG signal and physiological data (such as exhaled CO2 and Oxygen saturation (SpO2)) were simultaneously recorded. Subjects had to lie down with eyes closed staying awake. Two tasks were performed, each for a duration of 6 minutes. In the first one, the subjects had to breath normally while all signals were recorded. We referred to this task as free breathing (FB) task. In the second one, after a minute of FB, subjects had to alternate 30 seconds of voluntary breath hold and 30 seconds of FB (five times to reach the 6 minutes period). We referred to this task as breath hold (BH) task. All the acquisitions were conducted under controlled conditions and the subjects were previously trained to perform the 30 seconds BH. Indeed, they had to hold their breath feeling any discomfort or excessive air hunger avoiding great movements. For this reason, inspiratory BH is preferable as compared to expiratory BH. To start the BH period, an operator gave a signal to the subject simply touching his leg. To terminate the task, the operator touched again the leg’s subject. The experimental protocol was approved by the Ethical Committee of the University of Pisa-Pisa University Hospital, Pisa (Italy). The recordings were carried out in agreement with the Declaration of Helsinki. Written informed consent was obtained from all subjects.

EEG signal and physiological data acquisition

A 64 EEG device (Compumedics Neuroscan, SynAmps RT) was used. The electrodes were mounted into an elastic cap according to the standard 10–20 system. The EEG device also included two electrodes for ocular movement detection and two for the registration of the electrocardiographic signal. A reference channel was located between CZ and PZ, while the ground channel was situated between FPZ and FZ. The impedance of each electrode was maintained below 30 kΩ during the all acquisitions. The signal was acquired using low-pass filtered at 400 Hz and a sampling rate of 1 kHz. Exhaled CO2 was recorded using a CO2 analyzer (Cosmoplus; Novametrics) and SpO2 was recorded with a pulse oximeter (Pulsox-7; Minolta). All the data were digitized through a National Instrument acquisition card and an home-made software written in Java and developed in our institution.

EEG processing

The recorded EEG signals were analysed using the proprietary software Curry Neuroimaging Suite 7. All channels were re-referenced to the average signal. A baseline correction was applied to remove a constant or linear DC offset from the data. All signals were filtered using a band pass filter between 1 and 30 Hz. The channels with low quality signal were excluded from the analysis. Blink and cardiac artefacts were detected with threshold method and reduced using a Principal Component Analysis (PCA) method47. A visual inspection of the processed signals was performed. The signal intervals showing not reducible movement artefacts were detected and excluded from the analysis. A team of Neurologists assessed the quality of the remaining EEG signal for the further analysis. In MATLAB (MathWorks, Natick MA), the spectrogram of each channel was computed applying an Hanning window of 2 seconds with overlapping of 1 second. Nine different areas were extracted dividing the cap into three different sections (left L, middle M and right R) and further dividing into three rostrocaudal regions (anterior A, central C and posterior P). The nine areas were named as left anterior (LA), middle anterior (MA), right anterior (RA), left central (LC), middle central (MC), right central (RC), left posterior (LP), middle posterior (MP) and right posterior (RP). The local field power of each area was found averaging the power of all channels in the area of interest. Two EEG power bands were analysed, such as delta (1–4 Hz) and alpha (8–13 Hz) bands. It was demonstrated that these EEG frequency bands are sensitive to hypercapnic stimulation25,26. Finally, EEG power signals were linearly detrended and resampled at 50 Hz.

Physiological Parameters

Starting from the recorded CO2 signal, PETCO2 was extracted as maximum value of CO2 at the end of each expiration. A cubic spline model was use to interpolate the CO2 values and in particular, to estimate the PETCO2 also during BH period. To optimize the synchronization between PETCO2 and EEG signals, as for EEG power, PETCO2 was linearly detrended and resampled at 50 Hz. SpO2 was recorded and use to verify whether the task produce some effects on oxygen blood level.

Maximal Information Coefficient (MIC)

To consider only the contribution of the brain-respiratory slowly components, EEG power signals and respiratory signals were smoothed using a zero-phase moving averaged filter of 10 s48. To quantify the generic, i.e. linear and nonlinear, relationship between EEG power and PETCO2, Maximal Information Coefficient (MIC) was calculated37. MIC meets two heuristic properties (as generality and equitability) that allow to observe both functional and no functional relationship with a score that roughly equals the coefficient of determination (R2) of the data relative to the regression function37,38,49. Generally, considering two variable data x and y, if a relationship between each other exist, a grid on the scatter plot of the two variables can be created. First of all, the MIC algorithm finds the xy grid (G) with the highest induced mutual information. For each resolution, the best grid and the normalized score are stored to compile the characteristic matrix M = (mx,y) where every mx,y is the highest normalized mutual information of any x, y grid. Visualizing this matrix as surface, MIC represents the highest point. Formally, for a grid G, I G is the mutual information of the probability distribution on that particular grid G and mx,y can be derived as

$${m}_{x,y}=\frac{max\{{I}_{G}\}}{log\,min\{{m}_{x,y}\}}$$
(1)

Considering that the sample size is n and B is a function of the sample size (B = n0.6), MIC can be defined as:

$$MIC=\mathop{{\rm{\max }}}\limits_{xy < B}({m}_{x,y})$$
(2)

To test the statistical significance of the MIC, we performed surrogate data analysis as described in37. Briefly, surrogate data were created choosing 500 random permutations of EEG signal and PETCO2. The critical values of MIC, corresponding to α = 0.05, were estimated from the 95th percentile of the values obtained from random permutations. To evaluate the weight of the nonlinear component of the interaction between the two variables, MIC-ρ2 was estimated, where ρ2 is the Pearson coefficient. This index is always smaller that MIC, and it was proposed for the detection of nonlinear relationships, being less sensitive to linear interactions than the MIC coefficients37. We have to stress that even in the case of a MIC-ρ2 close to zero, a linear coupling between variables cannot be excluded. For these reasons, the joint analysis of MIC-ρ2 and MIC indexes, is useful to investigate the nature of the interaction. For instance, if a high value of MIC and a concomitant low value of MIC-ρ2 are observed, the interaction is likely to be mainly linear. On the other hand, if high values of MIC and MIC-ρ2 are observed the weight of the linear component is lower with respect to the non linear one.

Statistical Analysis

The comparison between FB and BH tasks were performed both for MIC and MIC-ρ2. Specifically, statistical significance was evaluated using non-parametric Wilcoxon signed rank test (W)50. The null hypothesis is that the differences between FB and BH tasks both in MIC as well as MIC-ρ2 come from a distribution with zero median. Scatter plots of MIC-ρ2 vs MIC, observed for each subject, will be drawn to explore the relevance of linear and nonlinear interactions. Since, MIC is always larger than MIC-ρ2, the scatter plot will lie below the bisector. If for a given subject, the pure non-linear component will differ from the generic (linear and non linear) relationship, the corresponding point in the scatter plot will move from the bisector. As a measure of the difference between the two indexes across the different subjects, the distance between the points of scatter plot and the bisector of the Cartesian plane (i.e. corresponding to equal values of MIC and MIC-ρ2) will be evaluated for subject, condition and brain area. The statistical difference of this measure between the FB and BH tasks, will be evaluated with a Wilcoxon signed rank test.

Data availability

The raw EEG data of this study are not publicly available due to ethical restrictions, however they can be reasonable requested from the corresponding author. All data generated from the raw EEG data (i.e., correlation results) are included in the Supplementary Information files.

References

1. 1.

Giannoni, A., Morelli, M. S. & Francis, D. P. Pathophysiology of central apneas in heart failure. Mathematical models, animal and clinical studies. In Emdin, M., Giannoni, A. & Passino, C. (eds) The Breathless Heart - Apneas in Heart Failure, chap. 4, 355 (Springer, 2017).

2. 2.

Grodins, F. S., Buell, J. & Bart, A. J. Mathematical analysis and digital simulation of the respiratory control system. J. applied physiology 22, 260–276 (1967).

3. 3.

Carley, D. W. & Shannon, D. C. A minimal mathematical model of human periodic breathing. J. applied physiology 65, 1400–1409 (1985).

4. 4.

Khoo, M. C., Kronauer, R. E., Strohl, K. P. & Slutsky, A. S. Factors inducing periodic breathing in humans: a general model. J. applied physiology: respiratory, environmental exercise physiology 53, 644–659 (1982).

5. 5.

Cherniack, N. S. & Longobardo, G. S. Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders. Exp. physiology 91, 295–305 (2006).

6. 6.

Horgan, J. & Lange, D. Analog computer studies of periodic breathing. IRE Transactions on Bio-Medical Electron. 9, 221–228 (1962).

7. 7.

Longobardo, G. S., Cherniack, N. S. & Fishman, A. P. Cheyne-Stokes breathing produced by a model of the human respiratory system. J. applied physiology 21, 1839–1846 (1966).

8. 8.

Mackey, M. & Glass, L. Oscillation and chaos in physiological control systems. Sci. 197, 287–289 (1977).

9. 9.

Pattinson, K. et al. Determination of the human brainstem respiratory control network and its cortical connections in vivo using functional and structural imaging. NeuroImage 44, 295–305 (2009).

10. 10.

Guyenet, P. & Bayliss, D. Neural Control of Breathing and CO2 Homeostasis. Neuron 87, 946–961 (2015).

11. 11.

Van den Aardweg, J. G. & Karemaker, J. M. Influence of chemoreflexes on respiratory variability in healthy subjects. Am. journal respiratory critical care medicine 165, 1041–7 (2002).

12. 12.

Giannoni, A. et al. Combined increased chemosensitivity to hypoxia and hypercapnia as a prognosticator in heart failure. J. Am. Coll. Cardiol. 53, 1975–80 (2009).

13. 13.

Evans, K. C. Cortico-limbic circuitry and the airways: Insights from functional neuroimaging of respiratory afferents and efferents. Biol. Psychol. 84, 13–25 (2010).

14. 14.

Mckay, L. C., Evans, K. C., Frackowiak, R. S. J. & Corfield, D. R. Neural correlates of voluntary breathing in humans. J. Appl. Physiol. 95, 1170–1178 (2003).

15. 15.

McKay, L. C., Adams, L., Frackowiak, R. S. J. & Corfield, D. R. A bilateral cortico-bulbar network associated with breath holding in humans, determined by functional magnetic resonance imaging. NeuroImage 40, 1824–32 (2008).

16. 16.

Heck, D. H. et al. Cortical rhythms are modulated by respiration. bioRxiv (2016).

17. 17.

Musizza, B. et al. Interactions between cardiac, respiratory and EEG-delta oscillations in rats during anaesthesia. The J. Physiol. 580, 315–26 (2007).

18. 18.

Sicard, K. M. & Duong, T. Q. Effects of hypoxia, hyperoxia, and hypercapnia on baseline and stimulus-evoked BOLD, CBF, and CMRO2 in spontaneously breathing animals. NeuroImage 25, 850–8 (2005).

19. 19.

Driver, I. D., Whittaker, J. R., Bright, M. G., Muthukumaraswamy, S. D. & Murphy, K. Arterial CO2 Fluctuations Modulate Neuronal Rhythmicity: Implications for MEG and fMRI Studies of Resting-State Networks. J. Neurosci. 36, 8541–8550 (2016).

20. 20.

Bloch-Salisbury, E., Lansing, R. & Shea, S. A. Acute changes in carbon dioxide levels alter the electroencephalogram without affecting cognitive function. Psychophysiol. 37, 418–26 (2000).

21. 21.

Thesen, T. et al. Depression of cortical activity in humans by mild hypercapnia. Hum. Brain Mapp. 33, 715–726 (2012).

22. 22.

Zappe, A. C., Uludag, K., Oeltermann, A., Ugurbil, K. & Logothetis, N. K. The Influence of Moderate Hypercapnia on Neural Activity in the Anesthetized Nonhuman Primate. Cereb. Cortex 18, 2666–2673 (2008).

23. 23.

Jones, M., Berwick, J., Hewson-Stoate, N., Gias, C. & Mayhew, J. The effect of hypercapnia on the neural and hemodynamic responses to somatosensory stimulation. NeuroImage 27, 609–623 (2005).

24. 24.

Matakas, F., Birkle, J. & Cervós-Navarro, J. The effect of prolonged experimental hypercapnia on the brain. Acta Neuropathol. 41, 207–210 (1978).

25. 25.

Xu, F. et al. The influence of carbon dioxide on brain activity and metabolism in conscious humans. J. Cereb. Blood Flow & Metab. 31, 58–67 (2010).

26. 26.

Wang, D. et al. Comparing the effect of hypercapnia and hypoxia on the electroencephalogram during wakefulness. Clin. neurophysiology 126, 103–109 (2015).

27. 27.

Hall, E. L. et al. The effect of hypercapnia on resting and stimulus induced MEG signals. NeuroImage 58, 1034–1043 (2011).

28. 28.

Kastrup, A., Krüger, G., Neumann-Haefelin, T. & Moseley, M. E. Assessment of cerebrovascular reactivity with functional magnetic resonance imaging: comparison of CO(2) and breath holding. Magn. resonance imaging 19, 13–20 (2001).

29. 29.

Baruah, R. et al. Novel cardiac pacemaker-based human model of periodic breathing to develop real-time, pre-emptive technology for carbon dioxide stabilisation. Open heart 1 (2014).

30. 30.

McKay, L. C., Janczewski, W. A. & Feldman, J. L. Sleep-disordered breathing after targeted ablation of preBötzinger complex neurons. Nat. neuroscience 8, 1142–4 (2005).

31. 31.

Eckert, D. J., Jordan, A. S., Merchia, P. & Malhotra, A. Central sleep apnea: Pathophysiology and treatment. Chest 131, 595–607 (2007).

32. 32.

Naughton, M. T. Respiratory sleep disorders in patients with congestive heart failure. J. thoracic disease 7, 1298–310 (2015).

33. 33.

Eckert, D. J. & Malhotra, A. Pathophysiology of adult obstructive sleep apnea. Proc. Am. Thorac. Soc. 5, 144–53 (2008).

34. 34.

Schellart, N. A. & Reits, D. Voluntary breath holding affects spontaneous brain activity measured by magnetoencephalography. Undersea & hyperbaric medicine: journal Undersea Hyperb. Med. Soc. Inc 26, 229–34 (1999).

35. 35.

Rodin, E. & Funke, M. Cerebral electromagnetic activity in the subdelta range. J. clinical neurophysiology: official publication Am. Electroencephalogr. Soc. 23, 238–44 (2006).

36. 36.

Morelli, M. et al. A Cross-Correlational Analysis between Electroencephalographic and End-Tidal Carbon Dioxide Signals: Methodological Issues in the Presence of Missing Data and Real Data Results. Sensors 16, 1828 (2016).

37. 37.

Reshef, D. N. et al. Detecting novel associations in large data sets. Sci. (New York, NY) 334, 1518–1524 (2011).

38. 38.

Zhang, Z., Sun, S., Yi, M., Wu, X. & Ding, Y. MIC as an appropriate method to construct the brain functional network. BioMed research international 2015, 825136 (2015).

39. 39.

Dong, L. et al. Simultaneous EEG-fMRI: trial level spatio-temporal fusion for hierarchically reliable information discovery. NeuroImage 99, 28–41 (2014).

40. 40.

Valenza, G. et al. Combining EEG Activity and Instantaneous Heart Rate for Assessing Brain-Heart Dynamics during Visual Emotional Elicitation in Healthy Subjects. Philos. Transactions Royal Soc. A 374 (2016).

41. 41.

Glass, L. Dynamical disease: Challenges for nonlinear dynamics and medicine. Chaos: An Interdiscip. J. Nonlinear Sci. 25, 097603 (2015).

42. 42.

Morelli, M. S. et al. Correlational analysis of electroencephalographic and end-tidal carbon dioxide signals during breath-hold exercise. In 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 6102–6105 (IEEE, 2015).

43. 43.

Morelli, M. S. et al. Exploratory analysis of nonlinear coupling between EEG global field power and end-tidal carbon dioxide in free breathing and breath-hold tasks. In 2016 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 728–731 (IEEE, 2016).

44. 44.

Hudson, A. L. et al. Electroencephalographic detection of respiratory-related cortical activity in 1 humans: from event-related approaches to continuous connectivity evaluation. J Neurophysiol 115, 2214–23 (2016).

45. 45.

Burki, N. K. & Lee, L.-Y. Mechanisms of dyspnea. Chest 138, 1196–201 (2010).

46. 46.

Knyazev, G. G. EEG delta oscillations as a correlate of basic homeostatic and motivational processes. Neurosci. & Biobehav. Rev. 36, 677–695 (2012).

47. 47.

Urigüen, J. A. & Garcia-Zapirain, B. EEG artifact removal-state-of-the-art and guidelines. J. neural engineering 12, 31001 (2015).

48. 48.

Yuan, H., Zotev, V., Phillips, R. & Bodurka, J. Correlated slow fluctuations in respiration, EEG, and BOLD fMRI. NeuroImage 79, 81–93 (2013).

49. 49.

Speed, T. A Correlation for the 21st Century. Sci. 334 (2011).

50. 50.

Glover, T. & Mitchell, K. An Introduction to Biostatistics: Third Edition (Waveland Press, 2015).

Author information

Authors

Contributions

M.S.M., A.Gi., M.E. and N.V. conceived the experiments; M.S.M. and N.V. conducted the experiments; M.S.M., A.Gr., E.P.S. and G.V. analysed the results. All authors reviewed the manuscript.

Corresponding author

Correspondence to Maria Sole Morelli.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

Morelli, M., Greco, A., Valenza, G. et al. Analysis of generic coupling between EEG activity and PETCO2 in free breathing and breath-hold tasks using Maximal Information Coefficient (MIC). Sci Rep 8, 4492 (2018). https://doi.org/10.1038/s41598-018-22573-6

• Accepted:

• Published:

• Breath-hold task induces temporal heterogeneity in electroencephalographic regional field power in healthy subjects

• Maria Sole Morelli
• , Nicola Vanello
• , Alejandro Luis Callara
• , Valentina Hartwig
• , Michelangelo Maestri
• , Enrica Bonanni
• , Michele Emdin
• , Claudio Passino
•  & Alberto Giannoni

Journal of Applied Physiology (2021)

• The neuronal associations of respiratory-volume variability in the resting state

• , Pierre LeVan
•  & J. Jean Chen

NeuroImage (2021)

• Adaptative mechanism of the equilibrative nucleoside transporter 1 (ENT-1) and blood adenosine levels in elite freedivers

• M. Marlinge
• , D. Vairo
• , A. Bertaud
• , C. Vernet
• , M. Chefrour
• , L. Bruzzese
• , M. C. Chaptal
• , G. Mottola
• , A. Boussuges
• , J. J. Risso
• , M. Blot-Chabaud
• , M. Coulange
• , R. Guieu
•  & F. Joulia

European Journal of Applied Physiology (2021)

• Detecting Associations Based on the Multi-Variable Maximum Information Coefficient

• Taoyong Gu
• , Jiansheng Guo
• , Zhengxin Li
•  & Sheng Mao

IEEE Access (2021)

• Ld-EEG Effective Brain Connectivity in Patients With Cheyne-Stokes Respiration

• Alejandro L. Callara
• , Maria Sole Morelli
• , Valentina Hartwig
• , Luigi Landini
• , Alberto Giannoni
• , Claudio Passino
• , Michele Emdin
•  & Nicola Vanello

IEEE Transactions on Neural Systems and Rehabilitation Engineering (2020)