Modeling Endotracheal Tube Resistance in Respiratory System and its Effects on Gas Exchange during Pressure-Controlled Mechanical Ventilation

Abstract

This study investigates the impact of endotracheal tube (ETT) size, on alveolar pressures of carbon dioxide CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> $\left(\mathrm{P}_{\mathrm{A}} \mathrm{CO}_{2}\right)$ and oxygen $\mathrm{O}_{2}\left(\mathrm{P}_{\mathrm{A}} \mathrm{O}_{2}\right)$ during mechanical Pressure Controlled Ventilation (PCV). Comprehending the interplay among these parameters is essential for enhancing patient outcomes and ventilator performance. The study utilized mathematical modeling and simulation in the Simulink MATLAB environment of the respiratory system compliance ($\mathrm{C}_{\mathrm{rs}}$), and resistance ($\mathrm{R}_{\mathrm{rs}}$), with the five ETT resistances using linear (Poiseuille’s law) and nonlinear (Rohrer equation) models during PCV for five respiratory frequencies ($\mathbf{F r}$). The internal diameter sizes of ETT are $6.5,7,7.5,8$, and 9 mm. The study unveiled significant differences in $\mathrm{P}_{\mathrm{A}} \mathrm{O}_{2}$ and $\mathrm{P}_{\mathrm{A}} \mathrm{CO}_{2}$ levels across, resistance models of ETT, and Fr. Notably, $\mathrm{P}_{A} \mathrm{O}_{2}$ levels exhibited substantial variation between linear and nonlinear models, with lower values in the nonlinear model. Increased ETT size was associated with improved oxygenation, while nonlinear resistance yielded lower $\mathbf{P}_{\mathrm{A}} \mathrm{O}_{2}$ levels. Conversely, $\mathrm{P}_{\mathrm{A}} \mathrm{CO}_{2}$ levels were higher in the nonlinear model. The results underscore the importance of considering ETT size, resistance models, and respiratory frequency when optimizing mechanical ventilation strategies. The nonlinear resistance model, representing a more physiologically accurate depiction of the respiratory system, led to differences in $\mathrm{P}_{\mathrm {{A}}} \mathrm{O}_{2}$ and $\mathrm{P}_{\mathrm {{A}}} \mathrm{CO}_{2}$ levels. Larger ETTs enhanced oxygenation but led to increased CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> retention. This study provides valuable insights into the complex interplay of factors influencing gas exchange during mechanical ventilation. Understanding these interactions is essential for optimizing ventilation strategies and improving patient outcomes in clinical practice.