## 3 Results
(Different colors correspond to the different 6 patients). Overall, the parameter estimates from the three models provide valuable insights into the mechanical properties of the respiratory system. The fractional-order impedance model demonstrates superior performance in capturing the complex viscoelastic behavior of lung tissues, as evidenced by its lower error metrics and consistent parameter estimates. The [PERSON] and Warburg models, while useful in specific contexts, exhibit higher variability and may be more sensitive to individual differences and measurement conditions. These findings suggest the importance of selecting appropriate models, which are based on the specific characteristics of the respiratory system being studied. In Figure 9, the tissue damping (\(G_{r}\)), tissue elastance (\(H_{r}\)), and tissue hysteresivity (\(\eta\)) for both the 4P-FOT (Figure 9A) and RESMON (Figure 9B) devices are given. The damping factor is a material characteristic that indicates its ability to absorb energy. In materials such as polymers, which exhibit properties similar to lung tissue, damping primarily results from viscous tissue properties, i.e., the strain response lagging behind the applied stresses [13]. Significant changes in \(G_{r}\) or \(H_{r}\) parameters indicate enhanced or altered secretions that cause dysfunction in small airways. Changes in \(H_{r}\) will induce changes in tissue elastance. Figure 8: Results of models identified and model performance representation for the measurements performed with the RESMON device. **(a)** Genetic algorithm optimization. **(b)** Measured (blue circles) and fitted model (1). **(c)** Model identification results using model (1) for all subjects. **(d)** Model identification results using model (5) for all subjects. **(e)** Model identification results using model (4) for all subjects. **(f)** Boxplot representation of the three model employed to fit the measured data. (Different colors correspond to the different 6 patients). The tissue damping parameter (\(G_{r}\)) reflects the energy dissipation within the lung tissues, with the 4P-FOT measurements showing relatively consistent Gr values across subjects, indicating similar viscoelastic properties at low frequencies. In contrast, Resmon measurements exhibit greater variability in \(G_{r}\), suggesting that high-frequency measurements are more sensitive to individual differences in tissue damping properties. The tissue elastance parameter (\(H_{r}\)) represents the stiffness of the lung tissues, with the 4P-FOT measurements revealing moderate variability in \(H_{r}\) among subjects, which may be attributed to differences in lung compliance and airway resistance. Resmon measurements show higher \(H_{r}\) values with greater variability, indicating that high-frequency oscillations capture a broader range of elastance-related characteristics, potentially influenced by central airway properties and inertial effects. The tissue hysteresivity parameter (\(\eta_{r}\)), the ratio of tissue damping to tissue elastance, characterizes the heterogeneity of the lung tissue. 4P-FOT measurements show relatively low and consistent (\(\eta_{r}\)) values across subjects, reflecting uniform viscoelastic behavior at low frequencies. The Resmon measurements display higher \(\eta_{r}\) values with significant variability, suggesting that high-frequency measurements are more sensitive to heterogeneous tissue properties and regional differences within the lungs. Changes in \(G_{r}\) and \(H_{r}\) indicate alterations in tissue composition and mechanics, relevant for conditions such as fibrosis and emphysema, while variations in (\(\eta_{r}\)) can provide insights into the degree of tissue heterogeneity, crucial for diagnosing and managing obstructive lung diseases. Figures 10-12 present the spectrograms of HR data for intervals 1 to 24, measured using the EQV sensor. The spectrograms offer a comprehensive view of the temporal and frequency characteristics of the HR signals over the two-hour monitoring period.