Analysis of Sigmoidal Equations To Describe the Pulmonary Pressure- Volume Curve in Acute Respiratory Distress Syndrome

Pulmonary pressure-volume curves (P-V curves) of patients with acute lung injury are commonly analyzed using a parametric algorithm with symmetrical properties. Some of the aspects observed after performing nonlinear regression for two models capable of fitting symmetric, respectively asymmetric data are discussed. One analyzed aspect was the algebraic complexity of the asymmetric model that does not allow for an estimation of the boundaries of the zone of maximal compliance directly from the parameter estimates in contrast to the symmetric model. Moreover, mathematical evidence is provided. Using a sigmoid equation for analysis of P-V curves a systematic deviation caused by asymmetrical distribution was encountered, leading to non-robust definitions of lower and upper inflection points. Increasing the number of parameters to fit asymmetric data does not increase physiological expression. We conclude that some of the drawbacks in using P-V curves may be attributed to imprecise analysis tools. To increase the value of P-V curves other forms of mathematical analysis should be investigated.