## 3 Results  
In Figure 7, the results obtained for the models introduced in Section 2.3 for the data recorded with the 4P-FOT device are depicted. The results presented in Figure 7 provide a comparative analysis of three investigated models, optimized using genetic algorithms. Figure 7 highlights the convergence of the genetic algorithm, demonstrating its efficacy in parameter optimization. The good fit between the measured data and the fractional-order model (1) indicates that the model accurately captures the properties of the respiratory system, suggesting that it has high fidelity in representing physiological phenomena (Figure 7b for one subject and Figure 7c for all subjects). The results obtained for the fractional-order impedance models in (4) and (5) are depicted in Figure 7d,e, respectively. These results also indicate a relatively good performance. The boxplot comparison of the error metrics shown in Figure 7f reveals that while all three models exhibit strong performance, the fractional-order impedance model given by (1) globally achieves the lowest error. The additional advantage of this particular type of fractional-order impedance model is that its parameters and its structure were extensively linked to anatomical and structural properties of the human lung [13]. In Figure 8, the results obtained for the identified models using the data measured with the RESMON are shown. The results presented in Figure 8 provide a comparative analysis of three investigated models, optimized using genetic algorithms. Figure 8 highlights the convergence of the genetic algorithm. The model fitting for the fractional-order impedance models from (1) for one subject is shown in Figure 8b and for all subjects in Figure 8c. The results obtained for the models from (4) and (5) are depicted in Figure 8d,e, respectively. Figure 8f illustrates the comparison of the error metrics between the models by means of a boxplot representation. Again, also in the case of high frequencies, it can be concluded that the fractional-order impedance model from (1) delivers the best performance. Identified model parameter values for the fractional-order, Cole, and Warburg models, respectively, for both the FOT and RESMON devices, are displayed in Tables 1-3. The results indicate that the fractional-order impedance model from (1) provides a good fit for both low-frequency and high-frequency measurements, with lower standard deviations suggesting consistent parameter estimation across subjects. The parameter values reflect the viscoelastic properties of lung tissues, with differences between the FOT and Resmon measurements highlighting the sensitivity of each method to different aspects of respiratory mechanics. The Cole model's parameters exhibit higher variability compared to the fractional-order model, particularly in the high-frequency Resmon measurements. This variability may be due to the model's sensitivity to high-frequency components and individual differences in respiratory \begin{table}
\begin{tabular}{l c c c c} \hline
**ID** & **Age (Years)** & **Weight (kg)** & **Height (cm)** & **BMI (kg/m\({}^{2}\))** \\ \hline
1 & 37 & 53 & 165 & 19 \\
2 & 40 & 85 & 180 & 26 \\
3 & 28 & 62 & 160 & 24 \\
4 & 35 & 78 & 172 & 26 \\
5 & 29 & 90 & 179 & 28 \\
6 & 28 & 51 & 163 & 19 \\ \hline \end{tabular}
\end{table} 
Table 4: Biometric parameters of the volunteers. impedance responses. The [PERSON] model's parameters show notable differences between subjects, particularly in high-frequency Resmon measurements. Figure 7: Results of models identified and model performance representation for the measurements performed with the 4P-FOT 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 (4) for all subjects. (**e**) Model identification results using model (5) for all subjects. (**f**) Boxplot representation of the three model employed to fit the measured data.