A Lumped Parameter Model of Airway/Lung Mechanics

Silvia Marconi1 and Claudio De Lazzari2
1Institute of Clinical Physiology, 2National Research Council


Abstract

Introduction: In this work we present a nonlinear lumped parameter mod-el of the airway/lung mechanics. The model is able to reproduce the time evolution of the fundamental variables (pressure, flow and volume) within each compartment of the respiratory system during normal breathing. A par-ticular attention is given to the pleural pressure that is the driving force of the system. Methods: Lungs are considered as a unique alveolar region connected to the external environment by means of the airways which divide into the up-per airway, the collapsible airway and the small airways. The pneumatic-electrical analogy allows to represent the respiratory system by employing an electrical circuit composed by four resistances, two capacitors and a genera-tor. The resistances simulate the friction of air in the airways and the lung tis-sue viscous property. The capacitors simulate the lung and the collapsible airway compliances which express their elasticity, i.e. their ability to expand when a pressure change occurs. All these elements are defined by nonlinear analytical expressions. The generator simulates the pleural pressure (Ppl) which drives the respiration process. The governing equations of the model are nonlinear first order ordinary differential equations. The model has been tested with three pleural pressure waveforms reproducing the regular breath-ing and two kinds of quiet breathing. Results: The response of the model to each Ppl waveform is analyzed in terms of flow, volumes and pressures. In particular, the simulation results show how the different pleural pressure waveforms influence the time evolu-tion of air flow, alveolar volume and flow-volume loop. Conclusions: The model presented in this work can be a tool for the de-scription of the main physiological quantities involved in the respiration with the final goal of a complete description of the respiratory system and its in-teraction with the cardiovascular system.