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Research Papers

Optimal Determination of Respiratory Airflow Patterns for a General Multicompartment Lung Mechanics System With Nonlinear Resistance and Compliance Parameters

[+] Author and Article Information
Saing Paul Hou

Singapore Institute
of Manufacturing Technology,
A*STAR,
Singapore 638075
e-mail: housp@SIMTech.a-star.edu.sg

Nader Meskin

Assistant Professor
Electrical Engineering Department,
Qatar University,
Doha 2713, Qatar
e-mail: nader.meskin@qu.edu.qa

Wassim M. Haddad

Professor
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: wm.haddad@aerospace.gatech.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 17, 2015; final manuscript received September 8, 2015; published online October 6, 2015. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(12), 121014 (Oct 06, 2015) (15 pages) Paper No: DS-15-1223; doi: 10.1115/1.4031596 History: Received May 17, 2015; Revised September 08, 2015

In this paper, we develop a framework for determining optimal respiratory airflow patterns for a multicompartment lung mechanics system with nonlinear resistance and compliance parameters. First, a nonlinear multicompartment lung mechanics model that accounts for nonlinearities in both the airway resistances and the lung compliances is developed. In particular, we assume that the resistive losses are characterized by a Rohrer-type model with resistive losses defined as the sum of linear and quadratic terms of the airflow. The proposed model is more realistic than those presented in the literature, since it takes into account the heterogeneity of lung anatomy and function as well as the nonlinearity of lung resistance and compliance parameters. This model can be used to provide a better understanding of pulmonary function as well as the process of mechanical ventilation. Next, using the proposed nonlinear multicompartment lung model, we develop a framework for determining optimal respiratory airflow patterns. Specifically, an optimization criterion that involves the minimization of the oxygen consumption of the lung muscles 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 is formulated and solved. The solution to the formulated optimization problem is derived using classical calculus of variation techniques. Finally, several illustrative numerical examples are presented to illustrate the efficacy of the proposed nonlinear multicompartment lung model and the corresponding optimal airflow patterns. Comparison with experimental data shows that our nonlinear resistance model predicts the airflow patterns more accurately than linear resistance models. Moreover, the optimization criterion used in this paper also provides a more accurate prediction of the optimal airflow patterns.

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Topics: Air flow , Lung
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Figures

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Fig. 3

Original and smoothed compliance functions

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Fig. 2

Typical inspiration and expiration compliance functions as a function of compartmental volumes

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Fig. 1

Four-compartment lung model

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Fig. 5

Responses of the two-compartment lung model with nonlinear resistances and compliances and the two-compartment lung model with linear resistances and nonlinear compliances subject to the same applied pressures

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Fig. 8

Volume and airflow rate patterns for different values of α2 with α1 = 2 and α3 = 0.03

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Fig. 9

Total lung volume and airflow rate patterns for different values of α3 with α1 = 2 and α2 = 0.05

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Fig. 4

Volume flow rate patterns for both models and recorded volume flow rate patterns of a ventilated patient from Ref. [38]. The maximum out-flow rate is approximately two (respectively, five) times that of the maximum in-flow rate for the nonlinear (respectively, linear) resistance model. The recorded maximum out-flow rate from Ref. [38] is approximately two times that of the maximum in-flow rate.

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Fig. 6

Total lung volume and airflow rate versus time

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Fig. 7

Total lung volume and airflow rate patterns for different values of α1 with α2 = 0.05 and α3 = 0.03

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Fig. 10

Total lung volume, airflow rate, and input pressure generated by optimal solution versus time. Solid line represents optimal patterns from our model and dotted line represents the optimal patterns from Ref. [28].

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