A Theory for Wheezing in Lungs
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), but the underlying physical mechanism responsible for the sounds is still poorly understood. The main purpose of this thesis is to change this, developing a theory for the onset of wheezing using both experimental and analytical approaches, with implications for both scientific understanding and clinical diagnosis.
Wheezing is caused by a fluid structure interaction between the airways and the air flowing through them. We have developed the first systematic set of experiments of direct relevance to this physical phenomena. We have also developed new tools in shell theory using geometric algebra to improve our physical understanding of the self-excited oscillations observed when air flows through flexible tubes.
In shell theory, the use of rotors from geometric algebra has enabled us to develop improved physical understanding of how changes of curvature, which are of direct importance to constitutive laws, come about. This has enabled a scaling analysis to be applied to the self-excited oscillations of flexible tubes, showing for the first time that bending energy is dominated by strain energy. We made novel use of multiple camera reconstruction to validate this scaling analysis by directly measuring the bending and strain energies during oscillations. The dominance of strain energy allows a simplification of the governing shell equations.
We have developed the first theory for the onset of self-excited oscillations of flexible tubes based on a flutter instability. This has been validated with our experimental work, and provides a predictive tool that can be used to understand wheezing in the airways of the lung.
Our theory for the onset of wheezing relates the frequency of oscillation to the airway geometry and material properties. This will allow diagnoses based on wheezing sounds to become more specific, which will allow the stethoscope, which has changed little in the last 200 years, to be brought into the 21st century.