A, Neuroanatomy of respiratory and pupillary rhythms. Respiratory pacemaker cells in the pre-Bötzinger complex (pBC) project to locus ceruleus (LC), which controls the global release of noradrenaline (NE), and to centromedial thalamus (CM). In a feedback loop, the incoming airstream of each breath triggers receptors reaching from the epithelium into the nasal cavity, propagating breathing-locked activity to the piriform cortex (PC) and mediodorsal thalamus (MD). The inset time series shows representative measurements of typical respiratory and pupil dynamics over the course of 60 s. The blue respiration trace shows the clear rhythmicity of breathing. A rhythmic component is not immediately visible in the red pupil trace. The raw unprocessed pupil trace, also depicted in orange, still contains the typical blinks (spikes) that have been interpolated for analysis (see Materials and Methods for details). B, Spectral composition (power spectra) of 5 min resting pupil (red) and respiration (blue) time series. The shaded area shows SEM. C, Magnitude-squared coherence spectrum between pupil and respiration time series. Observed coherence (purple) plotted against coherence computed on surrogate pupil time series (gray). The black straight line shows a frequency range with significant differences (p < 0.05, cluster-based permutation test). D, Directed connectivity quantified with spectrally resolved Granger causality. The top panel shows respiration-to-pupil (solid line) and pupil-to-respiration (dashed line) influences. The straight line at the bottom with an asterisk indicates the frequency range where connectivity differs (cluster-based permutation statistic, p < 0.05). The bottom panel shows connectivity spectra obtained from a control analysis using the surrogate pupil time series. E, Power envelope correlations (Pearson's correlation coefficient) between respiration and pupil time series. The marked areas denote significant differences at p < 0.05 (uncorrected; but relaxed cluster criterion applied; see Materials and Methods).