## 2 Mechanical Ventilation Modes
It can therefore be understood that the total airway pressure (P\({}_{i}\)(t)) needed to provide a respiratory act is given by the sum of the pressure developed by the respiratory muscles and the pressure developed by the ventilator:  
\[\text{P}_{i}(\text{t})=\text{P}_{\text{vent}}(\text{t})+\text{P}_{\text{musc} }(\text{t})=\text{P}_{0}+\frac{\text{V}(\text{t})}{\text{C}_{\text{RS}}}+ \text{R}_{\text{insp}/\exp}\,\dot{\text{V}}(\text{t}) \tag{3}\]  
This is called the equation of motion for the respiratory system, and points out the parameters that define the respiratory mechanics (C\({}_{\text{RS}}\), R\({}_{\text{insp}}\), R\({}_{\text{exp}}\)), and the variables adjustable by the operator on the machine (P, V, V) and that, therefore, represent the control variables. We can then construct a mode of ventilation using these three basic components: (1) the control variable, (2) the breath sequence, and (3) the operational algorithm. The last is the feedback control system used by mechanical ventilators to deliver specific ventilatory patterns. Seven different control types have been evolved to date; the simplest is set-point control, in which the output of the ventilator automatically matches a constant operator pre-set input value [42]. Indeed, modern mechanical ventilators use closed-loop control to maintain consistent pressure and flow waveforms in the face of changing patient/system conditions [7,8]. Therefore, given two possible control variables (volume, pressure) and three breath sequences (CMV, IMV, CSV), there are five possible mechanical ventilation modes (Table 1). Thus, whereas modern lung ventilators offer different operating modes to be adopted according to the specific needs of the patient, the basic criterion for the choice of ventilation model is based on the patient's ability to breathe autonomously. Once the control variable has been established (the main variable that the ventilator control circuit manipulates to cause inspiration), the ventilator needs more information to know how to handle the inspiratory and expiratory phase, as breathing is a periodic event. This is possible through the application of phase variables. These are essential in order to define how the ventilator starts (trigger variable), maintains (limit variable), and ends (cycle variable) the inspiratory phase, and how it behaves during the expiration phase (baseline variable). Thus, a particular variable is measured and used to initiate, maintain, and terminate each phase. In this context, pressure, volume, flow, and time are referred to as phase variables. In fact, depending on how the phase variables are distributed between ventilator and patient, it is possible to distinguish the ventilation mode, as shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Control Variables** & **Breath Sequence** & **Ventilation Mode** & **Acronym** \\ \hline \multirow{3}{*}{Pressure} & CSV & Pressure Support & PS-CSV \\  & CMV & Pressure Control & PC-CMV \\  & IMV & Pressure Control & PC-IMV \\ \hline \multirow{2}{*}{Flow–Volume} & CMV & Volume Control & VC-CMV \\  & IMV & Volume Control & VC-IMV \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical ventilation modes, adapted from [42]. This paper focuses on the controlled mode, for which the mechanical ventilator performs 100% of the respiratory work, as these are the modes used on COVID-19 patients within the first 24 h of ICU stay.