Comparison of Three Different Mathematical Models Applied to Respiratory Mechanics During Bronchoconstriction

Abstract

The assessment of respiratory mechanics is usually made by mathematical models. The simplest and one of the most known models is the Linear Single-Compartment Model (LSCM). The main prerogative of LSCM is linearity. However, the respiratory system does not have a linear behavior under several circumstances and the objective of this work is to compare the LSCM with 2 nonlinear models. In order to fulfill these comparisons, 6 male Wistar rats were studied during bronchoconstriction. Using a commercial ventilator, the LSCM and two nonlinear variations of this model were applied during mechanical ventilation in basal and during two doses of methacholine (MCh) a bronchoconstrictor. The two nonlinear models were: (1) a volume-dependent single compartment model, which have a nonlinear term related to elastance; (2) a flow-dependent single compartment model, which have a nonlinear term related to resistance. This study evaluated the adjustment of models to the measured pressure value and the evaluation of these models was conducted using the F-ratio test, which is based in comparison of variances, and the Akaike criterion, that measures the difference between the model and the sample values. Through of the value of mean squared residual, the results indicate improvement at the approximation when we add the nonlinear terms in relation to the linear model, in most cases, mainly the volume-dependent single compartment model. And another result is that the Akaike criterion presented a more effective comparison during the evaluation than the F-ratio test.