Asthma and COPD are chronic respiratory diseases that fluctuate widely with regard to clinical symptoms and airway obstruction, complicating treatment and prediction of exacerbations. Time series of respiratory impedance obtained by the forced oscillation technique are a convenient tool to study the respiratory system with high temporal resolution. In previous studies it was suggested that power-law-like fluctuations exist also in the healthy lung and that respiratory system impedance variability differs in asthma. In this study we elucidate such differences in a population of well-characterized subjects with asthma ( n = 13, GINA 1+2), COPD ( n = 12, GOLD I+II), and controls ( n = 10) from time series at single frequency (12 min, f = 8 Hz). Maximum likelihood estimation did not rule out power-law behavior, accepting the null hypothesis in 17/35 cases ( P > 0.05) and with significant differences in exponents for COPD ( P < 0.03). Detrended fluctuation analysis exhibited scaling exponents close to 0.5, indicating few correlations, with no differences between groups ( P > 0.14). In a second approach, we considered asthma and COPD as dynamic diseases, corresponding to changes of unknown parameters in a deterministic system. The similarity in shape between the combined probability distributions of normalized resistance and reactance was quantified by Wasserstein distances and reliably distinguished the two diseases (cross-validated predictive accuracy 0.80; sensitivity 0.83, specificity 0.77 for COPD). Wasserstein distances between 3+3 dimensional phase space reconstructions resulted in marginally better classification (accuracy 0.84, sensitivity 0.83, specificity 0.85). These latter findings suggest that the dynamics of respiratory impedance contain valuable information for the diagnosis and monitoring of patients with asthma and COPD, whereas the value of the stochastic approach is not clear presently.
Graph Diffusion Wasserstein Distances
