Linear and nonlinear mathematical models for noninvasive ventilation

P. S. Crooke, J. R. Hotchkiss, J. J. Marini

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Two mathematical models are proposed for passive, noninvasive ventilation. Both models take the form of coupled ordinary differential equations that describe the volume in a single compartment lung. One model is linear and the other nonlinear; both models are derived from basic pressure balances in the lung-ventilator system. These models are also compared to a physical model using a test lung. Both the physical and mathematical models exhibit instabilities that appear to have important clinical implications. The simulations from these models, and the forms of their governing equations, suggest that the presence of an airway leak proximal to the airway opening during pressure support noninvasive ventilation may render this mode of ventilation dynamically unstable. The mathematical models are extended to incorporate a special type of nonpassive ventilation where the total cycle times of the ventilator depend on the inspiratory phases of these cycles.

Original languageEnglish (US)
Pages (from-to)1297-1313
Number of pages17
JournalMathematical and Computer Modelling
Issue number11-12
StatePublished - May 16 2002

Bibliographical note

Funding Information:
*Scientist Development Grantee of the American Heart Association. tSupported in part by HealthPartners Research Foundation. A website for simulators of the models discussed in this paper is located at the following URL http: //mss . math. Vanderbilt. edu/‘pscrooke/MSS/bm. html. The simulations are performed on a UNIX server running Muthe-maticu.


  • Iteration function
  • Mask leak
  • Noninvasive mechanical ventilation
  • Nonlinear model


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