Result: Linear and nonlinear mathematical models for noninvasive ventilation

Title:
Linear and nonlinear mathematical models for noninvasive ventilation
Authors:
CROOKE, P. S, HOTCHKISS, J. R, MARINI, J. J
Source:
Mathematical and computer modelling. 35(11-12):1297-1313
Publisher Information:
Oxford: Elsevier Science, 2002.
Publication Year:
2002
Physical Description:
print, 35 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Approximation et analyse numériques, Numerical approximation and analysis, Equations différentielles et équations aux dérivées partielles, problèmes aux valeurs limites, Ordinary and partial differential equations, boundary value problems, Ordinary and partial differential equations; boundary value problems, Equation différentielle, Differential equations, Equation dérivée partielle, Partial differential equations, Fuite, Leaks, Instabilité, Instability, Itération, Iteration, Iteracción, Masque, Masks, Modèle linéaire, Linear model, Modelo lineal, Modèle mathématique, Mathematical models, Modèle non linéaire, Non linear model, Modelo no lineal, Modèle physique, Physical model, Modelo físico, Modèle simulation, Simulation model, Modelo simulación, Méthode non invasive, Non invasive method, Método no invasivo, Simulation numérique, Digital simulation, Ventilation mécanique, Mechanical ventilation, Ventilación mecánica
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States
Pulmonary and Critical Care Medicine, Regions Hospital and University of Minnesota, St. Paul, MN 55101, United States
ISSN:
0895-7177
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=13694654
Rights:
Copyright 2002 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.13694654
Database:
PASCAL Archive

Further Information

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.