Mathematical models for pressure controlled ventilation of oleic acid-injured pigs

One-compartment, mathematical models for pressure controlled ventilation, incorporating volume dependent compliances, linear and nonlinear resistances, are constructed and compared with data obtained from healthy and (oleic acid) lung-injured pigs. Experimental data are used to find parameters in the mathematical models and were collected in two forms. Firstly, the P_e-V curves for healthy and lung injured pigs were constructed; these data are used to compute compliance functions for each animal. Secondly, dynamic data from pressure controlled ventilation for a variety of applied pressures are used to estimate resistance parameters in the models. The models were then compared against the collected dynamic data. The best mathematical models are ones with compliance functions of the form C(V) = a + bV where a and b are constants obtained from the P_e-V curves and the resistive pressures during inspiration change from a linear relation P_r = RQ to a nonlinear relation P_r = RQ^ε where Q is the flow into the one-compartment lung and ε is a positive number. The form of the resistance terms in the mathematical models indicate the possible presence of gas-liquid foams in the experimental data.