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

Philip S. Crooke, K. Kongkul, Y. Lenbury, A. B. Adams, C. S. Carter, J. J. Marini, J. R. Hotchkiss

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6 Scopus citations


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 Pe-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 Pe-V curves and the resistive pressures during inspiration change from a linear relation Pr = RQ to a nonlinear relation Pr = RQε 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 languageEnglish (US)
Pages (from-to)99-112
Number of pages14
JournalMathematical Medicine and Biology
Issue number1
StatePublished - 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.


  • Mathematical model
  • Oleic acid injury
  • Variable compliance


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