# In Vitro Estimation of Relative Compliance during High-Frequency Oscillatory Ventilation
## 4 Discussion  
The results of this study showed that during HFOV, it is possible to monitor changes in trend in respiratory system compliance by analysis of reactance. According to the models, even the very peripheral lung segment compliances propagated to the proximal value of the total respiratory system compliance [41]. We conducted an in vitro laboratory experiment using defined physical models of the respiratory system with various values of compliance and flow resistance. Using the processing of the pressure and flow signals, we calculated reactance of the ventilated physical model, and showed that changes in the reactance corresponded to changes in compliance of the model. The results show that it is possible to monitor compliance changes during HFOV on various levels of flow resistance. The Rp5 resistor simulated an increase in the airway resistance, and its addition to the physical model resulted in an increase in the value of the measured \(X_{\rm rs}\) when compared to ventilation of the same rigid container in the model without the added Rp5 resistor. The inertance of a tube of a circular cross-section is inversely proportional to its cross-section. When we added the Rp5 resistor into the model of the respiratory system, we created a narrowing, which not only increased the flow resistance, but also led to an increase of inertance \(L\), therefore increasing \(X_{\rm rs}\), as shown by Equation (1). Nevertheless, in clinical practice, no major change in airway resistance in ventilated patients is likely to occur during short periods of titrating _CDP_. Under this assumption, the effect of resistance on the assessment of changes in respiratory system compliance from \(X_{\rm rs}\) can be neglected. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(V\) (L) & \multicolumn{2}{c}{\(X_{\rm rs}\) with No Resistor} & \multicolumn{2}{c}{\(X_{\rm rs}\) with Added Resistor} \\ \hline  & **Mean** & **SD 1** & **Mean** & **SD 1** \\ \hline
54 & \(-5.82\) & 0.06 & \(-1.56\) & 0.17 \\
35 & \(-12.07\) & 0.05 & \(-8.26\) & 0.17 \\
25 & \(-18.76\) & 0.06 & \(-15.62\) & 0.17 \\ \hline \hline \end{tabular} 1  
\end{table} 
Table 1: Summary of the detected values of \(X_{\rm rs}\) (cmH\({}_{2}\)O-s/L). Figure 2: The waveform of \(X_{\rm rs}\) when ventilating a model of the respiratory system without an additional resistor (\(R=0\) cmH\({}_{2}\)O-s/L) and with an additional resistor (\(R=5\) cmH\({}_{2}\)O-s/L). Three glass containers with different volumes (25, 35, and 54 L) were ventilated with and without the resistor to mimic various compliance of the respiratory system. An in vitro experiment with a rigid-wall glass container allowed us to evaluate the method of \(X_{\text{rs}}\) analysis for the trend estimation of the respiratory system compliance under stable conditions. In previous studies, the analysis of the spectral density of pressure and flow in the ventilatory circuit was conducted within the experiment on small laboratory animals: rabbits and preterm lambs. Before applying the same method of \(X_{\text{rs}}\) analysis on data from large subjects, we wished to evaluate the method on the data acquired under the condition of well-defined and stable lung compliance corresponding to the lung compliance of pediatric and adult patients. Our results were in concordance with [20,28], and suggested that the method of \(X_{\text{rs}}\) analysis is also suitable for analysis of pulmonary mechanics of ventilated large laboratory animals. The values of the standard deviation of \(X_{\text{rs}}\) were very low (Table 1), which indicates a good robustness of the algorithm for \(X_{\text{rs}}\) calculation. The oscillation of \(X_{\text{rs}}\) around the average value was caused by the noise in the measured pressure and flow signals. Table 1 shows that the addition of the resistor into the ventilated system led to an increase in the value of the standard deviation of \(X_{\text{rs}}\).