Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 165946, 11 pages
Research Article

Optimal Determination of Respiratory Airflow Patterns Using a Nonlinear Multicompartment Model for a Lung Mechanics System

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA

Received 25 January 2012; Revised 2 April 2012; Accepted 4 April 2012

Academic Editor: Thierry Busso

Copyright © 2012 Hancao Li and Wassim M. Haddad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop optimal respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system. Specifically, we use classical calculus of variations minimization techniques to derive an optimal airflow pattern for inspiratory and expiratory breathing cycles. The physiological interpretation of the optimality criteria used involves the minimization of work of breathing and lung volume acceleration for the inspiratory phase, and the minimization of the elastic potential energy and rapid airflow rate changes for the expiratory phase. Finally, we numerically integrate the resulting nonlinear two-point boundary value problems to determine the optimal airflow patterns over the inspiratory and expiratory breathing cycles.