## 3 Operating Principles of Mechanical Vertilators for ICUs
\begin{table}
\begin{tabular}{c c c c} \hline
**Mode** & **Parameter** & **Symbol** & **Equation** \\ \hline \multirow{4}{*}{VC-CMV} & Tidal Volume (L) & \(\mathrm{V_{T}}\) & \(\mathrm{V_{T}=I_{pf}\ T_{i}}\) \\  & Mean Inspiratory Flow (L/s) & \(\mathrm{\dot{V}_{I}}\) & \(\mathrm{\dot{V}_{I}=\frac{60V_{i}}{1_{i}}}\) \\  & Plateau Pressure (cmH\({}_{2}\)O) & \(\mathrm{P_{plt}}\) & \(\mathrm{P_{plt}=P_{0}+\frac{V_{T}}{C_{ss}}}\) \\  & Insp. Peak Pressure (cmH\({}_{2}\)O) & PIP & \(\mathrm{PIP=P_{plt}+R_{imp}\ I_{pf}}\) \\ \hline \multirow{4}{*}{PC-CMV} & Tidal Volume (L) & \(\mathrm{V_{T}}\) & \(\mathrm{V_{T}=\Delta P\ \mathrm{C_{RS}}\big{(}1-e^{-\frac{1}{\tau_{i}}}\big{)}}\) \\  & Inspiratory Flow (L/s) & \(\mathrm{\dot{V}_{I}}\) & \(\mathrm{\dot{V}_{I}=\frac{\Delta P}{\mathrm{E_{app}}}\Big{(}e^{-\frac{1}{\tau_{ i}}}\Big{)}}\) \\  & Pressure Gradient (cmH\({}_{2}\)O) & \(\Delta P\) & \(\Delta P=\mathrm{PIP-PEEP}\) \\ \hline \multirow{4}{*}{Both modes} & Total Cycle Time (s) & TCT & TCT = \(\mathrm{T_{i}+T_{e}=\frac{60}{RR}}\) \\  & I:E ratio & I:E & I:E = \(\mathrm{\dot{T}_{i}}\) \\  & Inspiratory Time Constant (s) & \(\tau_{\mathrm{insp}}\) & \(\tau_{\mathrm{insp}}=\mathrm{R_{insp}\ C_{RS}}\) \\  & \(\mathrm{Expiratory\ Time\ Constant}\) (s) & \(\tau_{\mathrm{eep}}\) & \(\tau_{\mathrm{eep}}=\mathrm{R_{exp}C_{RS}}\) \\  & \(\mathrm{Expiratory\ Flow\ (L/s)}\) & \(\mathrm{\dot{V}_{E}=-\frac{\Delta P}{\mathrm{E_{app}}}\Big{(}e^{-\frac{1}{\tau_{ e}}}\Big{)}}\) \\  & Insp. Resistance (cmH\({}_{2}\)O / L/s) & \(\mathrm{R_{insp}}\) & \(\mathrm{R_{insp}=\frac{\Delta P}{\mathrm{V}}}\) \\  & Exp. Resistance (cmH\({}_{2}\)O / L/s) & \(\mathrm{R_{exp}}\) & \(\mathrm{R_{exp}=\frac{\Delta V}{\mathrm{V}}}\) \\  & Compliance (L/cmH\({}_{2}\)O) & \(\mathrm{C_{RS}}\) & \(\mathrm{C_{RS}=\frac{\Delta V}{\mathrm{V}}}\) \\  & Elastance (cmH\({}_{2}\)O / L) & \(\mathrm{E_{RS}}\) & \(\mathrm{E_{RS}=\frac{\Delta V}{\mathrm{C_{ss}}}}\) \\  & Mean Airway Pressure (cmH\({}_{2}\)O) & \(\mathrm{\overline{P}_{aw}}\) & \(\mathrm{k(PIP-PEEP)\Big{(}\frac{T_{i}}{T_{i}+T_{e}}\Big{)}-PEEP}\) \\ \hline \multirow{4}{*}{Primary Variable} & Pressure (cmH\({}_{2}\)O) & P & \\  & Volume (L) & V & \\ \cline{1-1}  & Flow (L/s) & \(\mathrm{\dot{V}}\) & \\ \cline{1-1}  & Inspiratory Time (s) & \(\mathrm{T_{i}}\) & \\ \cline{1-1}  & Expiratory Time (s) & \(\mathrm{T_{e}}\) & \\ \cline{1-1}  & Respiratory Rate (breaths/min) & RR & \\ \hline \end{tabular}
\end{table} 
Table 3: Equations relating the important parameters for VC-CMV and PC-CMV mode, adapted from [44]. compressors of various types [7]. The energy needed to expand the patient's lungs can alternatively be supplied by compressed gas from the wall outlets of the hospital (general range 2.5-7 bar). The electric power system has the advantage of being able to be used wherever there is an electrical source; however, as the electric motor consists of bearings and connecting rods in motion, it becomes unreliable if used for a prolonged period of time [11]. The distribution system, which consists of the patient circuit and the inspiratory and expiratory valves, allows the gas received by the power system to be conveyed from/to the patient's lungs. In addition to this purely mechanical function, it also performs the task of monitoring the development of ventilation by detecting the pressure and flow rate during respiration and reporting this to the control and setting system. Furthermore, after endotracheal intubation, the upper airway loses its capacity to heat and moisture inhaled gas, hence a humidifier is introduced into the distribution system [47]. Finally, the safety system is the part of the ventilator that ensures that there are no risk situations during ventilation for the patient by indicating them to the operator [7]. The pneumatic scheme, at the base of the Simulink code, is similar to that employed by the Galileo [12] and Drager Infinity V500 [13] intensive care ventilators, and is shown in Figure 12.  
Figure 11: Key components of ICU mechanical ventilators.