## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 99-112 |

Number of pages | 14 |

Journal | Mathematical Medicine and Biology |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - Mar 2005 |

### Bibliographical note

Funding Information:Kongkul was supported by Ministry of University Affairs, Thailand. Lenbury was supported by The Thailand Research Fund. Marini was supported in part by Health Partners Research Foundation and Hotchkiss is a Scientist Development Grantee of the American Heart Association.

## Keywords

- Mathematical model
- Oleic acid injury
- Variable compliance