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Research Papers

# Respiratory System Model for Quasistatic Pulmonary Pressure-Volume $(P-V)$ Curve: Inflation-Deflation Loop Analyses

[+] Author and Article Information
R. Amini, U. Narusawa

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115

J Biomech Eng 130(3), 031020 (May 09, 2008) (12 pages) doi:10.1115/1.2913343 History: Received May 23, 2007; Revised November 14, 2007; Published May 09, 2008

## Abstract

A respiratory system model (RSM) is developed for the deflation process of a quasistatic pressure-volume $(P-V)$ curve, following the model for the inflation process reported earlier. In the RSM of both the inflation and the deflation limb, a respiratory system consists of a large population of basic alveolar elements, each consisting of a piston-spring-cylinder subsystem. A normal distribution of the basic elements is derived from Boltzmann statistical model with the alveolar closing (opening) pressure as the distribution parameter for the deflation (inflation) process. An error minimization by the method of least squares applied to existing $P-V$ loop data from two different data sources confirms that a simultaneous inflation-deflation analysis is required for an accurate determination of RSM parameters. Commonly used terms such as lower inflection point, upper inflection point, and compliance are examined based on the $P-V$ equations, on the distribution function, as well as on the geometric and physical properties of the basic alveolar element.

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## Figures

Figure 2

(I) Alveolar element of the RSM for inflation process. (II) Alveolar element of the RSM for deflation process.

Figure 4

P-V curves and distribution functions for inflation limb of DG1

Figure 1

A typical P-V curve and parameters of continuous P-V model equations

Figure 3

P-V curves for DG1 and DG2

Figure 5

On determination of the RSM parameters. (a) DG1—before injury. Energy equation is not used as a constraint. I (solid): minimum total error (simultaneous inflation-deflation error minimization); II (dotted): minimum inflation error (inflation error minimization, followed by deflation error minimization). (b) DG1—after injury. Simultaneous inflation-deflation error minimization is applied. III (solid): energy equation not used. IV (dotted): energy equation used.

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