Temporal variations in the pattern of breathing: techniques, sources, and applications to translational sciences

Fig. 1. Visualization of the Rössler attractor, a continuous-time dynamical system that exhibits chaotic dynamics with fractal properties. The system is composed of three nonlinear differential equations and thus has three variables. a Temporal fluctuations of the x variable. Although each variable oscillates within a fixed range of values, its amplitude is highly variable. b Three-dimensional trajectory of the Rössler attractor visualized using the values of all three variables. c Three-dimensional plot of the Rössler attractor reconstructed using delay-time embedding (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau =30\,\mathrm{ a}.\mathrm{u}.$$\end{document}τ=30a.u.) of a single variable (x). Note that the complexity of the system is well preserved compared to b, in which all three variables are used. d Recurrence plot of the reconstructed attractor using delay-time embedding (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

Fig. 2. Visualization and quantification of the complexity of actual experimental data. The data, obtained from an open dataset [225], contain a human respiratory signal while the participant watched a scary video. The respiratory signal is the temporal change in chest dimension associated with the expansion and contraction of the chest cavity, which was measured using a Hall effect sensor placed high on the torso. a The temporal change in chest dimension, sampled at 10 Hz, was used as the x variable for attractor reconstruction (b) and to generate the recurrence plot (c). b Three-dimensional plots of an attractor reconstructed using delay-time embedding (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau =0.6\,\mathrm{ s})$$\end{document}τ=0.6s). Variables y and z represent respiratory signals 0.6 s and 1.2 s advanced relative to the x variable, respectively. c Recurrence plot of human respiration while the participant watched a scary video (\documentclass[12pt]{minimal} \usepackage{amsmath}…

Fig. 3. Representative calcium transients of EGFP-positive and EGFP-negative cells [79]. a Astrocytes are identified with GFAP promoter-controlled expression of EGFP. Scale bar: 40 µm. b Cross-correlation image between each pixel and the low-frequency calcium oscillation of cell #4 indicates that low-frequency astrocytic calcium oscillations are highly synchronized. c The top trace shows the respiratory rhythmic calcium fluctuation, and the other traces show bandpass filtered calcium signals of representative cells. For cells #1–8, the location of each cell is indicated in the left panels (a and b). For EGFP-positive cells (#1–5), the calcium signals of the cell (green) and its vicinity (light blue) are shown

Fig. 4. Schematic drawings of coupled slow and fast oscillators that exhibit cross-frequency coupling (CFC). a Slow glial (red circles) and fast neuronal (black circles) oscillators are organized within the pFRG and preBötC and modulate their intrinsic rhythms [75]. The pFRG and preBötC conditionally couple, resulting in complex variability, such as quantal slowing. b The slow respiratory oscillator (black circle) orchestrates fast neuronal oscillations (blue circles) in the anterior cingulate, premotor, insular, and hippocampal cortices via CFC [151, 152]. pFRG parafacial respiratory group, preBötC pre-Bötzinger complex, ACC anterior cingulate cortex, PMC premotor cortex, INS insular cortex, HPC hippocampal cortex

Fig. 5. Representative modes of cross frequency interactions. Consider a slow oscillator (a) that interacts with a fast oscillator (b). In c, the power of the fast oscillation is modulated by the phase of the slow oscillation. This mode of interaction can be observed between the phase of respiration (slow oscillation) and the power of the gamma-band (40–150 Hz) oscillations during attention to breathing [151], and between the phase of respiration and the power of alpha-band (8–13 Hz) oscillations during a near-threshold spatial detection task [147]. In d, the frequency of the fast oscillation is modulated by the phase of the slow oscillation