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,
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

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.

Copyright © 2015 by ASME
Topics: Air flow , Lung
Your Session has timed out. Please sign back in to continue.


Campbell, D. , and Brown, J. , 1963, “ The Electrical Analogue of the Lung,” British J. Anaesth., 35(11), pp. 684–692. [CrossRef]
Wald, A. A. , Murphy, T. W. , and Mazzia, V. D. , 1968, “ A Theoretical Study of Controlled Ventilation,” IEEE Trans. Biomed. Eng., 15(4), pp. 237–248. [CrossRef] [PubMed]
Epstein, M. A. F. , and Epstein, R. A. , 1979, “ Airway Flow Patterns During Mechanical Ventilation of Infants: A Mathematical Model,” IEEE Trans. Biomed. Eng., 26(5), pp. 299–306. [CrossRef] [PubMed]
Barbini, P. , 1982, “ Non-Linear Model of the Mechanics of Breathing Applied to the Use and Design of Ventilators,” ASME J. Biomed. Eng., 4(4), pp. 294–304. [CrossRef]
Marini, J. J. , and Crooke, P. S. , 1993, “ A General Mathematical Model for Respiratory Dynamics Relevant to the Clinical Setting,” Am. Rev. Respir. Dis., 147(1), pp. 14–24. [CrossRef] [PubMed]
Crooke, P. S. , Hota, S. , Marini, J. J. , and Hotchkiss, J. R. , 2003, “ Mathematical Models of Passive, Pressure-Controlled Ventilation With Different Resistance Assumptions,” Math. Comput. Model., 38(5), pp. 495–502. [CrossRef]
Chellaboina, V. , Haddad, W. M. , Li, H. , and Bailey, J. M. , 2010, “ Limit Cycle Stability Analysis and Adaptive Control of a Multi-Compartment Model for a Pressure-Limited Respirator and Lung Mechanics System,” Int. J. Control, 83(5), pp. 940–955. [CrossRef]
Jonson, B. , and Svantesson, C. , 1999, “ Elastic Pressure–Volume Curves: What Information Do They Convey?” Thorax, 54(1), pp. 82–87. [CrossRef] [PubMed]
Crooke, P. S. , Marini, J. J. , and Hotchkiss, J. R. , 2002, “ Modeling Recruitment Maneuvers With a Variable Compliance Model for Pressure Controlled Ventilation,” J. Theor. Med., 4(3), pp. 197–207. [CrossRef]
Volyanskyy, K. Y. , Haddad, W. M. , and Bailey, J. M. , 2011, “ Pressure- and Work-Limited Neuroadaptive Control for Mechanical Ventilation of Critical Care Patients,” IEEE Trans. Neural Networks, 22(4), pp. 614–626. [CrossRef]
Otis, A. B. , Fenn, W. O. , and Rahn, H. , 1950, “ Mechanics of Breathing in Man,” J. Appl. Physiol., 2(11), pp. 592–607. [PubMed]
Wood, L. , Engel, L. , Griffin, P. , Despas, P. , and Macklem, P. , 1976, “ Effect of Gas Physical Properties and Flow on Lower Pulmonary Resistance,” J. Appl. Physiol., 41(2), pp. 234–244. [PubMed]
Peslin, R. , Ying, Y. , Gallina, C. , and Duvivier, C. , 1992, “ Within-Breath Variations of Forced Oscillation Resistance in Healthy Subjects,” Eur. Respir. J., 5(1), pp. 86–92. [PubMed]
Tomalak, W. , Peslin, R. , and Duvivier, C. , 1998, “ Variations in Airways Impedance During Respiratory Cycle Derived From Combined Measurements of Input and Transfer Impedances,” Eur. Respir. J., 12(6), pp. 1436–1441. [CrossRef] [PubMed]
Younes, M. , Kun, J. , Masiowski, B. , Webster, K. , and Roberts, D. , 2001, “ A Method for Noninvasive Determination of Inspiratory Resistance During Proportional Assist Ventilation,” Am. J. Respir. Crit. Care Med., 163(4), pp. 829–839. [CrossRef] [PubMed]
Avanzolini, G. , Barbini, P. , Bernardi, F. , Cevenini, G. , and Gnudi, G. , 2001, “ Role of the Mechanical Properties of Tracheobronchial Airways in Determining the Respiratory Resistance Time Course,” Ann. Biomed. Eng., 29(7), pp. 575–586. [CrossRef] [PubMed]
Crooke, P. , Kongkul, K. , Lenbury, Y. , Adams, A. , Carter, C. , Marini, J. , and Hotchkiss, J. , 2005, “ Mathematical Models for Pressure Controlled Ventilation of Oleic Acid-Injured Pigs,” Math. Med. Biol., 22(1), pp. 99–112. [CrossRef] [PubMed]
Younes, M. , Puddy, A. , Roberts, D. , Light, R. , Quesada, A. , Taylor, K. , Oppenheimer, L. , and Cramp, H. , 1992, “ Proportional Assist Ventilation: Results of an Initial Clinical Trial,” Am. Rev. Respir. Dis., 145(1), pp. 121–129. [CrossRef] [PubMed]
Laubscher, T. , Heinrichs, W. , Weiler, N. , Hartmann, G. , and Brunner, J. , 1994, “ An Adaptive Lung Ventilation Controller,” IEEE Trans. Biomed. Eng., 41(1), pp. 51–59. [CrossRef] [PubMed]
Dojat, M. , Brochard, L. , Lemaire, F. , and Harf, A. , 1992, “ A Knowledge-Based System for Assisted Ventilation of Patients in Intensive Care Units,” Int. J. Clin. Monit. Comput., 9(4), pp. 239–250. [CrossRef] [PubMed]
Sinderby, C. , Navalesi, P. , Beck, J. , Skrobik, Y. , Comtois, N. , Friberg, S. , Gottfried, S. , and Lindstrom, L. , 1999, “ Neural Control of Mechanical Ventilation in Respiratory Failure,” Nat. Med., 5(12), pp. 1433–1436. [CrossRef] [PubMed]
Li, H. , and Haddad, W. M. , 2013, “ Model Predictive Control for a Multicompartment Respiratory System,” IEEE Trans. Control Syst. Technol., 21(5), pp. 1988–1995. [CrossRef]
Hou, S. P. , Meskin, N. , and Haddad, W. M. , 2014, “ Output Feedback Sliding Mode Control for a Linear Multicompartment Lung Mechanics System,” Int. J. Control, 87(10), pp. 2044–2055.
Mead, J. , 1960, “ Control of Respiratory Frequency,” J. Appl. Physiol., 15(3), pp. 325–336.
Yamashiro, S. , and Grodins, F. , 1971, “ Optimal Regulation of Respiratory Airflow,” J. Appl. Physiol., 30(5), pp. 597–602. [PubMed]
Hämäläinen, R. P. , and Viljanen, A. A. , 1978, “ A Hierarchical Goal-Seeking Model of the Control of Breathing I–II,” Biological Cybernetics, 29(3), pp. 151–166. [CrossRef] [PubMed]
Hämäläinen, R. P. , and Viljanen, A. A. , 1978, “ Modeling the Respiratory Airflow Pattern by Optimization Criteria,” Biol. Cybern., 29(3), pp. 143–149. [CrossRef] [PubMed]
Li, H. , and Haddad, W. M. , 2012, “ Optimal Determination of Respiratory Airflow Patterns Using a Nonlinear Multicompartment Model for a Lung Mechanics System,” Comput. Math. Methods Med., 2012, pp. 1–11.
Proctor, D. F. , Hardy, J. B. , and McLean, R. , 1949, “ Studies of Respiratory Air Flow; Significance of the Normal Pneumotachogram,” Bull. Johns Hopkins Hosp., 85(4), pp. 253–280. [PubMed]
Hämäläinen, R. P. , and Sipilä, A. , 1984, “ Optimal Control of Inspiratory Airflow in Breathing,” Optim. Control Appl. Methods, 5(2), pp. 177–191. [CrossRef]
Weibel, E. R. , 1963, Morphometry of the Human Lung, Academic, New York.
Hou, S. P. , Meskin, N. , and Haddad, W. M. , 2014, “ A General Multicompartment Lung Mechanics Model With Nonlinear Resistance and Compliance Respiratory Parameters,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 566–571.
Svantesson, C. , Sigurdsson, S. , Larsson, A. , and Jonson, B. , 1998, “ Effects of Recruitment of Collapsed Lung Units on the Elastic Pressure–Volume Relationship in Anaesthetised Healthy Adults,” Acta Anaesthesiol. Scandinavica, 42(10), pp. 1149–1156. [CrossRef]
Bitzén, U. , Niklason, L. , Göransson, I. , and Jonson, B. , 2010, “ Measurement and Mathematical Modelling of Elastic and Resistive Lung Mechanical Properties Studied at Sinusoidal Expiratory Flow,” Clin. Physiol. Funct. Imaging, 30(6), pp. 439–446. [CrossRef] [PubMed]
Dombi, J. , and Gera, Z. , 2005, “ The Approximation of Piecewise Linear Membership Functions and Łukasiewicz Operators,” Fuzzy Sets Syst., 154(2), pp. 275–286. [CrossRef]
Campbell, E. J. M. , Agostoni, E. , and Davis, J. N. , 1970, The Respiratory Muscles: Mechanics and Neural Control, Lloyd-Luke, London.
McGregor, M. , and Becklake, M. R. , 1961, “ The Relationship of Oxygen Cost of Breathing to Respiratory Mechanical Work and Respiratory Force,” J. Clin. Investig., 40(6), pp. 971–980. [CrossRef]
Georgopoulos, D. , and Roussos, C. , 1996, “ Control of Breathing in Mechanically Ventilated Patients,” Eur. Respir. J., 9(10), pp. 2151–2160. [CrossRef] [PubMed]
Bonmarchand, G. , Chevron, V. , Jusserand, D. , Girault, C. , Moritz, F. , Leroy, J. , Pasquis, P. , and Chopin, C. , 1996, “ Increased Initial Flow Rate Reduces Inspiratory Work of Breathing During Pressure Support Ventilation in Patients With Exacerbation of Chronic Obstructive Pulmonary Disease,” Intensive Care Med., 22(11), pp. 1147–1154. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Original and smoothed compliance functions

Grahic Jump Location
Fig. 1

Four-compartment lung model

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Fig. 6

Total lung volume and airflow rate versus time

Grahic Jump Location
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].



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In