Limits...
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.

Show MeSH
Phase portrait for x1*(t) versus x2*(t) and x1(t) versus x2(t).
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3376482&req=5

fig9: Phase portrait for x1*(t) versus x2*(t) and x1(t) versus x2(t).

Mentions: Figure 7 shows the driving pressure generated by the respiratory muscles using the optimal air volume eTx*(t), t ≥ 0. Figure 8 compares the optimal air volume trajectory eTx*(t), t ≥ 0, with a nonoptimal air volume trajectory eTx(t), t ≥ 0, generated by the linear pressure pin(t) = 20t + 5 cm H2O, t ∈ [0, Tin], and pex(t) = 0 cm H2O, t ∈ [Tin, Tin + Tex], [6]. Note that eTx*(t), t ≥ 0, switches between the end expiratory level eTV0 = 0.2 l and the tidal volume eTVT = 1.2 l. Figure 9 shows the phase portrait of the optimal trajectories x1*(t) and x2*(t) and suboptimal trajectories x1(t) and x2(t). Note that both sets of trajectories asymptotically converge to a limit cycle, with the optimal solutions satisfying the boundary conditions given in (18), (19), (28), and (29). Figure 10 compares the value of the total performance criterion generated by the optimal air volume with the value of the total performance criterion generated by the nonoptimal air volume.


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)

Phase portrait for x1*(t) versus x2*(t) and x1(t) versus x2(t).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig9: Phase portrait for x1*(t) versus x2*(t) and x1(t) versus x2(t).
Mentions: Figure 7 shows the driving pressure generated by the respiratory muscles using the optimal air volume eTx*(t), t ≥ 0. Figure 8 compares the optimal air volume trajectory eTx*(t), t ≥ 0, with a nonoptimal air volume trajectory eTx(t), t ≥ 0, generated by the linear pressure pin(t) = 20t + 5 cm H2O, t ∈ [0, Tin], and pex(t) = 0 cm H2O, t ∈ [Tin, Tin + Tex], [6]. Note that eTx*(t), t ≥ 0, switches between the end expiratory level eTV0 = 0.2 l and the tidal volume eTVT = 1.2 l. Figure 9 shows the phase portrait of the optimal trajectories x1*(t) and x2*(t) and suboptimal trajectories x1(t) and x2(t). Note that both sets of trajectories asymptotically converge to a limit cycle, with the optimal solutions satisfying the boundary conditions given in (18), (19), (28), and (29). Figure 10 compares the value of the total performance criterion generated by the optimal air volume with the value of the total performance criterion generated by the nonoptimal air volume.

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