Browsing by Author "Vuorela, Paul Erik"

Those who snore may suffer from sleep apnea, which causes a person to stop breathing during their sleep. This happens due to a collapse of the upper airway, which seals off the airflow partially or completely. A collapse like this is not necessarily dangerous in itself, as a person who experiences this usually wakes up briefly in order to breathe. These collapses do, however, result in bad sleep and may that way lead to other illnesses. That is why it is of interest to study this phenomenon, in order to improve the treatment of people who suffer from severe sleep apnea. Two mathematical models are analysed in the thesis. The focus of the models is on the breathing of humans and how the respiratory system functions when a patient may stop breathing. The first model in the thesis is used to study the airflow in the upper airway and the second model covers the carbon dioxide transport between alveoli, tissues and blood. The thesis also includes a biological background of the models, as well as explanations and definitions of the methods used when running computational simulations on them. A short analysis is made on the first model and a numerical analysis with some computational simulations is made on the second model. A basic understanding of derivation, partial derivation and the approximation of derivatives is needed for the mathematics used in the thesis.