Abstract
A quarter of the world's population experience wheezing. These sounds have been used for diagnosis since the time of the Ebers Papyrus (ca 1500 BC). We know that wheezing is a result of the oscillations of the airways that make up the lung. However, the physical mechanisms for the onset of wheezing remain poorly understood, and we do not have a quantitative model to predict when wheezing occurs. We address these issues in this paper. We model the airways of the lungs by a modified Starling resistor in which airflow is driven through thin, stretched elastic tubes. By completing systematic experiments, we find a generalized ‘tube law’ that describes how the cross-sectional area of the tubes change in response to the transmural pressure difference across them. We find the necessary conditions for the onset of oscillations that represent wheezing and propose a flutter-like instability model for it about a heavily deformed state of the tube. Our findings allow for a predictive tool for wheezing in lungs, which could lead to better diagnosis and treatment of lung diseases.
Highlights
Lung sounds offer a cheap, non-invasive, non-radioactive source of information on pathology in the upper chest [1], but diagnoses based on these sounds lack specificity [2] and repeatability [3,4]
We have used self-excited oscillations of stretched elastic tubes driven by an air flow as a model for wheezing in lungs
We have performed experiments with a wide range of flexible tubes with properties directly applicable to the lungs—short rubber tubes of various thicknesses and lengths held in various degrees of axial tension
Summary
Lung sounds offer a cheap, non-invasive, non-radioactive source of information on pathology in the upper chest [1], but diagnoses based on these sounds lack specificity [2] and repeatability [3,4]. In order to be relevant to the lung, a linear stability analysis would need to include the effects of axial pretension, consider tubes whose length is relatively short compared to their diameter (a length of four times the diameter or less is typical [9]), include the effects of the inertia of the tube walls (because air is the working fluid in the lung), and linearize about a strongly deformed tube state (this is one of the main observations of our work). Significant progress has been made in developing our theoretical understanding of Starling resistors, producing plenty of candidate mechanisms, but as yet quantitative predictions can not be made for the frequencies and flowrates at onset in the specific context of the lung. We propose a phenomenological model for the onset of wheezing
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