Saing Paul Hou Singapore Institute of Manufacturing Technology, A*STAR, Singapore 638075 e-mail: housp@SIMTech.a-star.edu.sg Nader Meskin 1 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 Optimal Determination of Respiratory Airflow Patterns for a General Multicompartment Lung Mechanics System With Nonlinear Resistance and Compliance Parameters In this paper, we develop a framework for determining optimal respiratory airflow pat- terns for a multicompartment lung mechanics system with nonlinear resistance and com- pliance 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 mechani- cal ventilation. Next, using the proposed nonlinear multicompartment lung model, we de- velop 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 minimiza- tion 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 nu- merical examples are presented to illustrate the efficacy of the proposed nonlinear multi- compartment 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 crite- rion used in this paper also provides a more accurate prediction of the optimal airflow patterns. [DOI: 10.1115/1.4031596] 1 Introduction Human lungs are vulnerable to critical illness and as a conse- quence, respiratory failure is common for patients in intensive care units. Respiratory failure is the loss of the respiratory sys- tem’s ability to maintain oxygen and/or carbon dioxide within normal ranges. In this case, mechanical ventilation is needed to provide an adequate exchange of oxygen and carbon dioxide in order for the organs to function normally. Numerous mathemati- cal models of respiratory function have been developed in the hope of better understanding pulmonary function and the process of mechanical ventilation [1–5]. However, the models that have been presented in the medical and scientific literature have typi- cally assumed homogeneous lung function. For example, in anal- ogy to a simple electrical circuit, the most common model has assumed that the lungs can be viewed as a single compartment characterized by its compliance (the ratio of compartment volume to pressure) and the resistance to airflow into the compartment [1,2,5,6]. Lungs, especially diseased lungs, are heterogeneous, both func- tionally and anatomically, and are composed of many subunits or compartments, which differ in their capacities for gas exchange. Therefore, the simplistic single compartment model cannot adequately represent the lung mechanics system, and hence, sty- mie the accurate diagnosis of pulmonary diseases and the develop- ment of efficient mechanical ventilation. Accurate and realistic models should take this heterogeneity into account. A model for a multicompartment lung mechanics system has been developed in Ref. [7], where it is assumed that the resistive pressure losses are linear functions of airflows (i.e., constant airway resistances) and the lung compliances are constant over the entire range of lung volumes. However, clinical data show that the lung compliances are not constant over the entire range of lung volumes [8]. Specifi- cally, for low lung volumes the compliance is low and linearly increases with increasing volume; however, at a particular value a transition region is entered wherein the compliance is constant. Then, when the lung volume exceeds a particular value, the com- pliance starts decreasing. A single compartment lung model using a piecewise linear compliance–volume relationship is developed in Ref. [9]. Building on the results of Ref. [9], a multicompart- ment lung model with linear resistances and nonlinear complian- ces is given in Ref. [10]. However, it is well established in the fluid mechanics literature that for laminar flow through a tube, the pressure loss is a linear function of the flow, whereas for turbulent flows, the pressure loss is a nonlinear function of the flow. Thus, an accurate model repre- senting the lung mechanics should take into account nonlinearities 1 Corresponding 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. 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