Journal Article

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

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

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 22, issue 1, pages 99-112
Published in print March 2005 | ISSN: 1477-8599
Published online March 2005 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqh023
Mathematical models for pressure controlled ventilation of oleic acid-injured pigs

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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 PeV 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 PeV 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.

Keywords: oleic acid injury; mathematical model; variable compliance

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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