Analysis of the mechanisms of expiratory asynchrony in pressure support ventilation: a mathematical approach

A mathematical model was developed to analyze the mechanisms of expiratory asynchrony during pressure support ventilation (PSV). Solving the model revealed several results. 1) Ratio of the flow at the end of patient neural inspiration to peak inspiratory flow (VTI/V-peak) during PSV is determined by the ratio of time constant of the respiratory system (tau) to patient neural inspiratory time (TI) and the ratio of the set pressure support (Pps) level to maximal inspiratory muscle pressure (Pmusmax). 2) VTI/V-peak is affected more by tau/TI than by Pps/Pmus max. VTI/Vpeak pancreases in a sigmoidal relationship to tau/TI. An increase in Pps/ Pmus max slightly shifts the VTI/V-peak-tau/TI curve to the right, i.e., VTI/V-peak becomes lower as Pps/Pmus max increases at the same tau/TI. 3) Under the selected adult respiratory mechanics, VTi/V-peak ranges from 1 to 85% and has an excellent linear correlation with tau/TI. 4) In mechanical ventilators, single fixed levels of the flow termination criterion will always have chances of both synchronized termination and asynchronized termination, depending on patient mechanics. An increase in tau/TI causes more delayed and less premature termination opportunities. An increase in Pps/Pmus max narrows the synchronized zone, making inspiratory termination predisposed to be in asynchrony. Increasing the expiratory trigger sensitivity of a ventilator shifts the synchronized zone to the right, causing less delayed and more premature termination. Automation of expiratory trigger sensitivity in future mechanical ventilators may also be possible. In conclusion, our model provides a useful tool to analyze the mechanisms of expiratory asynchrony in PSV.