Optimal determination of respiratory airflow patterns using a nonlinear multi-compartment model for a lung-rib-cage system

In this paper, we develop optimal respiratory airflow patterns using a nonlinear multi-compartment model for a lung-rib-cage 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 involve 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.