## Abstract

A general mathematical model for the dynamic behavior of the two-compartment respiratory system in response to an arbitrary applied inspiratory pressure is investigated. The model is used to compute explicit expressions for ventilation and pressure variables of clinical interest, for clinician-selected and impedance-determined inputs. The outcome variables include tidal volume, end-expiratory pressure, minute ventilation, mean alveolar pressure for each compartment, given resistive parameters and compliances of the system. The calculation of these outcome variables assume that the patient is ventilated under passive conditions. Limiting values of the outcome variables as the frequency of the breathing cycle increases are also computed for three basic types of ventilation: constant, linear, and sinusoidal pressure waveforms. Explicit expressions for the limiting values of certain ratios of the key outcome variables (tidal volume, end-expiratory pressure, and mean alveolar pressure) are computed and are shown to be independent of the applied airway pressure.

Original language | English (US) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Mathematical and Computer Modelling |

Volume | 24 |

Issue number | 7 |

DOIs | |

State | Published - Oct 1996 |

Externally published | Yes |

### Bibliographical note

Funding Information:in part by a subcontract to Vanderbilt University from the Ramsey Foundation, by DHHS Gtsny No. IP50-HL50152-01 and the Hamsey Foundation.

## Keywords

- Limiting values
- Lung
- Mathematical model
- Mechanical ventilation
- Two-compartment