Mathematics as a means to stop snoring

Streamlines illustrating the paths taken by a selection of virtual, airborne dust particles flowing into the nose and down through the upper airway, during inspirational flow. The streamlines are colored to reflect the air speed (Blue=slow < green < yellow < red=fast).

24. September 2013

A flag waving in the wind can illustrate what we call "air-solids interaction". When the wind hits the top of the flagpole the flag dances to the wind's rhythms, often in complex ways. And as we all know: it takes two to tango. The air-flow is also influenced by the flag's movements; the direction and speed of air-flow changes along the flag's surface. This constitutes what is known as a two-way fluid-structure interaction (FSI).

A more evident example of FSI is literally right in front of us. Whereas some people can take a deep breaths and sleep tight, others may find them self in a completely different situation. Their nose- and respiratory tract causes them to, when they draw their breath, to snore. When we're awake the muscles keep the respiratory tract open. When we're asleep, however, the muscles relax and the soft tissue in the upper part of the tract begins to behave like a flag in the wind. Snoring occurs when the soft parts of the respiratory tract is deformed so much that the airway momentarily is completely closed.

Snoring In some cases, snoring becomes so severe that it constitutes a medical problem. The most severe form of snoring is called obstructive sleep apnea syndrome and affects 2-4 percent of the population. This syndrome is characterized by heavy snoring, frequent pauses in breathing, gasping for breath and frequent awakening. In the most serious cases, apnea may occur hundreds of times a night, which leads to a reduced oxygen consumption. Low oxygen consumption can lead to reduced quality of life, an increased chance of getting sick and increased mortality. Sleep apnea is also connected to low concentration, and children show signs of hyperactivity and may have learning and behavioral difficulties.

There are a variety of treatments for sleep apnea, depending on the severity level, but the medical staff only have their past experience and judgment to base their decisions on when choosing a type of treatment. Today there are no available tools to help predict the outcome of treatment. Worst case: the surgical treatment could worsen the situation rather than help.

Researchers in flow engineering at SINTEF Materials and Chemistry, desire to help improve treatment for those struggling with sleep-related breathing disorders. As of today, no one knows exactly how the respiratory system is affected by the airflow. There is no method that measures the elasticity of the mucous membranes and soft tissues of living patients. In collaboration with researchers at NTNU and St. Olav's Hospital, we want to establish mathematical models to illustrate what happens in the airways where sleep apnea occurs.

To obtain reliable mathematical models work interdisciplinary work is required, combining theoretical knowledge with experiments, measurements and medical examinations. The finished mathematical models can be used to predict the effectiveness of treatment methods, and the aim is to create an indispensable tool for medical personnel when determining the best treatment option for each patient.