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Mathematical Medicine and Biology 1998 15(4):321-337; doi:10.1093/imammb/15.4.321
© 1998 by Institute of Mathematics and its Applications
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Patient–ventilator interaction: A general model for nonpassive mechanical ventilation

P. S. CROOKE {dagger}, J. D. HEAD, J. J. MARINI {ddagger} and J. R. HOTCHKISS

Department of Mathematics, Vanderbilt University Nashville, TN 37240, USA
Division of Pulmonary and Critical Care Medicine, University of Minnesota Minneapolis, MN 55455, USA

A general mathematical model for the dynamic behaviour of a single-compartment respiratory system in response to an arbitrary applied inspiratory airway pressure and arbitrary respiratory muscle activity 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, average pleural pressure, as well as the work performed by the ventilator and the respiratory muscles. It is also demonstrated that under suitable conditions, there is a flow reversal that can occur during inspiration.

Keywords: mechanical ventilation; nonpassive ventilation; respiratory muscle pressure; pulmonary model


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