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Optimal determination of respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system.

Li H, Haddad WM - Comput Math Methods Med (2012)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

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

ABSTRACT
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.

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Single-compartment lung model.
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Related In: Results  -  Collection


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fig1: Single-compartment lung model.

Mentions: First, for simplicity of exposition, we consider a single-compartment lung model as shown in Figure 1. In this model, the lungs are represented as a single lung unit with nonlinear compliance c(x) connected to a pressure source by an airway unit with resistance (to airflow) of R. At time t = 0, a driving pressure pin(t) is applied to the opening of the parent airway, where pin(t) is generated by the respiratory muscles or a mechanical ventilator. This pressure is applied over the time interval 0 ≤ t ≤ Tin, which is the inspiratory part of the breathing cycle. At time t = Tin, the applied airway pressure is released and expiration takes place passively, that is, the external pressure is only the atmospheric pressure pex(t) during the time interval Tin ≤ t ≤ Tin + Tex, where Tex is the duration of expiration.


Optimal determination of respiratory airflow patterns using a nonlinear multicompartment model for a lung mechanics system.

Li H, Haddad WM - Comput Math Methods Med (2012)

Single-compartment lung model.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3376482&req=5

fig1: Single-compartment lung model.
Mentions: First, for simplicity of exposition, we consider a single-compartment lung model as shown in Figure 1. In this model, the lungs are represented as a single lung unit with nonlinear compliance c(x) connected to a pressure source by an airway unit with resistance (to airflow) of R. At time t = 0, a driving pressure pin(t) is applied to the opening of the parent airway, where pin(t) is generated by the respiratory muscles or a mechanical ventilator. This pressure is applied over the time interval 0 ≤ t ≤ Tin, which is the inspiratory part of the breathing cycle. At time t = Tin, the applied airway pressure is released and expiration takes place passively, that is, the external pressure is only the atmospheric pressure pex(t) during the time interval Tin ≤ t ≤ Tin + Tex, where Tex is the duration of expiration.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

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

ABSTRACT
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.

Show MeSH