Two Operational Modes of Cardio-Respiratory Coupling Revealed by Pulse-Respiration Quotient

Figure 10. Bar plots showing the group mean ± standard deviation of different correlation or aggregation measures. (a,b) Related to BBI vs. PRQ correlations: (a) slopes of linear regression lines (sl); (b) Pearson’s coefficients (rp); (c–n) quantities related to BBI vs. mRRI correlations which measure the degree of aggregation of points around PRQint lines. Left side—with respect to four states; right side—with respect to the scatter plots characterized with aggregation (AG) or a random (RD) distribution of points. The statistical test results are displayed in Table 1.

Figure 1. Two scatter plots of the BBI vs. PRQ correlations in two different subjects. (a) A case study with quantized PRQ values; (b) a case study with continual point distributions. Blue—supine; red—standing; black—supine, with slow 0.1 Hz breathing; green—standing with slow 0.1 Hz breathing. Linear regression slopes (sl); Y—intercepts (yint). Pearson’s coefficient of linear correlation (r) and regression significance (p) are also indicated for the four states, respectively, in the order indicated above.

Figure 2. Examples of two types of scatter plots (BBI and mRRI) obtained from subjects #1 and #2 in supin and stand01 experimental conditions, respectively. (a) Subject #1 (supin), with pronounced quasi-linear clusters; (b) subject #2 (stand01), with no apparent clusters and with points randomly scattered. Upper right corner: ri—the integral (not cluster-averaged) coefficient of linear correlation is low and bears little physiological relevance; p is the corresponding significance level of ri.

Figure 3. (a) The same data as seen in Figure 2a, with concurrent PRQint lines added. Solid lines represent PRQint; dashed lines are used for PRQint ± 0.5, representing the cluster borders; (b,c) shows the same data as in Figure 2a,b, respectively, drawn with (mRRI)r, referring only to integer parts of PRQ values, according to Equation (3), and showing that all scattering information is thereby lost.

Figure 4. Example scatter plots: (a) with an aggregation of points around the concurrent PRQint lines; (b) with a random distribution of points. Pwtot—the percentage of points that lie within the gradually widening sectors, with a half-width of w, calculated for all clusters simultaneously, according to Equation (5); Pr—the same quantity of uniformly distributed points; Pdtot—their difference according to Equation (6); wmax—the half-width where the maximum of Pdtot occurs.

Figure 5. Examples of fitting the experimentally derived points Pwtot(w) (open circles) with the model Pwmtot(w) using Equation (9) (solid line). Four estimates for the quality of fitting are also given: error of fitting (err), square error per point (err2/N), R-square adjusted (R2adj), and Akaike’s information criterion (AICc). (a) An example showing pronounced aggregation, where Pwtot(w) > Pr; (b) another example close to a random distribution of points, wherePwtot(w) ≈ Pr.

Figure 6. Diagram showing the group scatter plot of correlations between BBI and PRQ, where the results from twenty subjects in four states were superimposed. Each dot represents the result for one BB interval. The group linear regression for each state is drawn as a solid line: blue—supine; red—standing; black—supine, with slow 0.1 Hz breathing; green—standing, with slow 0.1 Hz breathing. Linear regression slopes (sl) with Y-intercepts (yint). Pearson’s coefficients of linear correlation (r) and regression significance (p, showing very high significance) are indicated as well, ordered from left to right as: supin, stand, supin01, and stand01.

Figure 7. Four examples of subjects exhibiting different patterns of clustering, with high intra-cluster correlations of BBI vs. mRRI data. (a) Subjects where the scatter plots had clusters in all four experimental conditions; (b) subjects with clusters appearing only in the supine body position; (c) clusters appearing only in the case of spontaneous breathing; (d) subjects with no visible high-correlation clusters. The integral state-related Pearson’s coefficients (ri) and the corresponding correlation significances (p) are also shown. Each dot corresponds to one BB interval. Color coding is explained in (a).

Figure 8. Group scatter plot of respiratory BBI vs. mRRI (averaged RRI within each BBI), obtained by superimposing separate scatter plots of all twenty subjects in all four states (supine—blue; standing—red; supine with slow 0.1 Hz breathing—black; standing with slow 0.1 Hz breathing—green). The concurrent PRQint lines are also plotted.

Figure 9. (a,c) The pulse–respiration quotient as a function of the BBI serial number (i.e., time, shown in black lines and black circles), with an arbitrarily chosen time interval colored in red; (b,d) the same data are presented as scatter plots of (BBI and mRRI) points. (a,b) Example of a PRQ time plot and the corresponding scatter plot, with pronounced clustering; (c,d) a PRQ time plot and its scatter plot, with a random distribution of points. The arrows in (b) indicate the directions of the point dynamics.

Figure 11. (a–f) Histograms approximating the distributions of 80 (20 subjects × 4 states) BBI vs. mRRI scatter plots over six proposed measures of aggregation of the points around the PRQint lines. Corresponding PDE distributions are drawn as red solid curves. Except in the case of rav, all other five measures were pointing to two types of scatter plots (AG and RD), which is in accordance with the results in Figure 10 and Table 1 and can be assumed by the previous visual observation. Inlets show the correlations between a particular measure and (std(PRQ))av, where each dot represents one scatter plot, color-coded to correspond to one of two visually assessed subtypes (AG or RD).

Figure 12. (a,b) Bar plots showing the results of the linear averaging of b1max (mean ± standard deviation); (c,d) (b1a)g—doubly angularly averaged from b1(i))s, according to Equations (10) and (11), across all BBI(i) and all subjects (s); the error bars represent the circularly corrected standard deviations (b1hst)c. (a,c) Statistics of the scatter plots in four experimental states; (b,d) the scatter plots shown according to the type of aggregation.