Fig. 1

A Schematic representation of the volume at end-inspiration (Vei), which is the volume at end-expiration (Vee) above the functional residual capacity plus tidal volume, measured after prolonged apnea. B Schematic representation explaining the rationale of the formula to estimate Vei, with pressure on the x-axis and volume on the y-axis. In a patient with dynamic pulmonary hyperinflation inspiration starts from the total amount of positive end-expiratory pressure (PEEP_total). PEEP_total can be obtained by performing an end-expiratory occlusion maneuver (i.e., zero flow conditions, after an occlusion of a few seconds PEEP_total represents the alveolar pressure). If applied PEEP by the ventilator is 0 cmH₂O, which is the case in the current study, PEEP_total represents intrinsic PEEP (PEEP_i). The patient inhales a certain volume (Vt) reaching an inspiratory pressure depending on the mechanical characteristics of the lung. By performing an end-inspiratory occlusion maneuver the plateau pressure (P_plateau) can be obtained, which corresponds to Vei. Compliance (C_rs) is defined as the slope of the volume − pressure relationship, e.g., the ratio of a change in volume and pressure, for the respiratory system this means: Vt/(P_plateau −PEEP_i) (1). From the figure it is clear that C_rs can also be calculated as Vei/P_plateau (2). Therefore, Vei is Vee plus Vt, but also C_rs times P_plateau (3). Combining [1], (2) and (3) gives Vei_formula = (Vt)/P_plateau–PEEP_i) * P_plateau (4) which can be rewritten as Vei_formula = (Vt * P_plateau)/(P_plateau –PEEP_i) (5). This rationale holds true when C_rs remains constant