Mathematical Modeling
RECRUITMENT
As an exploratory analysis, recruitment-to-inflation ratio values obtained in each derecruitment step were regressed (by nonlinear ordinary least-squares) against average step PEEP with a quadratic (parabolic) model, constrained to pass through the point (0,0), assuming essentially no recruitment at extremely low PEEP values. A goodness-of-fit test (chi-square) was conducted on each fit. Such an analysis was not prespecified and was included in the analysis during the peer review process.The rationale of performing such an exploratory analysis by introducing a nonlinear model is that of quantitatively identifying (where possible) the increasing and then decreasing recruitment at progressively increasing PEEP. This behavior is assumed to occur on physiologic principles: at zero end-expiratory pressure, by definition, there is no recruitment; recruitment must tend toward zero at very high PEEP as the maximal capacity of the lung–chest wall is reached on the pressure–volume curve of the respiratory system, corresponding to an ever-decreasing complianceIt should also be appreciated that this approach essentially makes statements about only one (out of possibly many) class of patients, whose data behave in possibly different ways. Indeed, only patients conforming to the increasing and then decreasing pattern are eventually characterized. A formal assessment of what classes actually exist and what (meta)parameters characterize each class (