## 2 Material and Methods  
### Forced Oscillation Technique  
At rest, normal breathing, such as that used during the Forced Oscillation Technique (FOT) lung function test, involves the contraction of the diaphragm, parasaternal muscles,and scaleni. During inhalation, the diaphragm moves downward, pulling the lower surfaces of the lungs with it. Exhalation occurs when these muscles relax. Variations in the elastic recoil of the lungs, which can make them more or less stiff, impact their normal functioning, particularly affecting total lung volume and the pressure-volume relationship. The shape and area under the pressure-volume loop provide information upon the mechanical workload of the respiratory system and is used for diagnosis [13].  
Lung function mechanics are evaluated by the FOT lung function test with a superimposed multisine of multiple frequencies, assessing the frequency response of the lung tissue and airways [13; 20]. This evaluation provides information known as respiratory impedance, a complex variable. The real part of respiratory impedance characterizes total resistance, while the imaginary part reflects the balance between inertive and compliant (reactance) mechanical properties [21]. Resistance and reactance, which are mathematically distinct contributions to respiratory system impedance, correlate with morphological changes in the lungs. These changes are represented by mechanical properties in the 4-50 Hz frequency interval [5; 22]. At frequencies below 5 Hz, impedance is predominantly influenced by the mechanical properties of the small peripheral airways and alveolar tissues. The FOT at low-frequency measurement involves superimposing a customized amplitude--frequency multisine signal onto the patient's natural breathing. The main advantages of FOT measurements include it being effortless, requiring minimal patient cooperation, which is especially beneficial for pediatric or critically ill patients; the frequency-dependent characteristics of impedance allow for the differentiation of obstructions within various lung structures; and impedance data offer insights into the pathophysiological changes in lung structure and function, which can be interpreted using specific mathematical models calibrated with real data.  
In this study, both low-frequency and high-frequency respiratory devices are employed to comprehensively evaluate respiratory function. The low-frequency prototype device (4P-FOT). This device was developed by the Dynamical Systems and Control (DySC) Research Group at Ghent University, located in Ghent, Belgium, depicted in Figure 1A, measuring in the frequency range of 0.05-5 Hz, provides detailed insights into the viscoelastic properties of the lungs and airway remodeling [10]. In contrast, the high-frequency commercial device (Resmon Pro Full) is depicted in Figure 1B. This device was manufactured by ResTech in Milano, Italy, and distributed by MGC Diagnostics, based in Minnesota, USA. It measures in the frequency range 5-37 Hz, and gives a broader analysis of airway resistance and reactance, capturing dynamic changes in respiratory mechanics under various physiological conditions [10]. Both devices offer complementary insights into respiratory mechanics. Therefore, it is ideal to combine the information provided from both.  
Figure 1: **(A)** Schematic of the 4P–FOT device principle of operation and related instrumentation. **(B)** Resmon PRO FULL device.