Marianne Wilcox
Marianne Wilcox and Prof. Allan Willms

It’s not quite counting sheep. But to learn more about a sleep disorder, Guelph grad student Marianne Wilcox used numbers at a Toronto sleep clinic and a model developed by U of G mathematicians.

For her master’s degree completed last year, she looked at Cheyne-Stokes respiration (CSR), a neurological condition that causes irregular breathing during sleep.

An estimated one in four Canadian adults is at high risk of developing sleep apnea, according to a 2009 survey by the Public Health Agency of Canada.

Sleep apnea is a condition that affects breathing during sleep. The most common kind is obstructive sleep apnea, caused when soft tissue in the back of the throat relaxes and blocks the airway. Central sleep apnea, including CSR, involves the central nervous system and occurs when the brain improperly signals muscles controlling breathing.

Cheyne-Stokes is often associated with heart failure or stroke and occurs more often in men than in women. One in two patients with congestive heart failure has this condition, says Wilcox.

People with Cheyne-Stokes often cycle during sleep from barely breathing to almost hyperventilating. Wilcox and her supervisor, Prof. Allan Willms, mathematics and statistics, hoped to learn whether body position affects that cycle.

Doctors believe lying down might trigger the condition and may be connected to blood pooling in areas of the body. Says Willms: “Does shifting of blood volume in various parts of the body explain the onset of these oscillations in someone who is susceptible to CSR?”

Wilcox found body position caused erratic breathing patterns in people with CSR but not a significant difference. Body position was less significant in the model than whether or not someone had suffered a stroke.

For this study, she and Willms extended a computer model developed by her master’s co-adviser, Prof. Bill Langford, and a previous student. The model uses blood volume data collected from various parts of the circulatory system, including the aorta, heart chambers, veins and arteries.

She used data from the Sleep Research Lab at the Toronto Rehabilitation Institute, connected with the University of Toronto.

Wilcox visited the Toronto lab along with several friends to be tested. They spent 90 minutes hooked up to electrodes while lying motionless as technicians periodically checked readings. “I thought it would be relaxing,” she says, “but it was so uncomfortable.”

Wilcox began her PhD last year. She completed a mathematics undergrad at Guelph in 2011.

Willms has used math on other biology problems, including working with neurobiologists on models of ion channels. Biomathematics also helped him in studies with a food scientist on E. coli contamination of ground beef and in research with a microbiologist on antibiotic resistance.

“It encourages me that math can provide some help in answering biological questions,” he says.

For her PhD, she is using biomath in cancer studies with pathobiology professor Byram Bridle. He studies cancer viral therapy in mice.

During a viral infection, the immune system produces proteins called cytokines. A cytokine “storm” can be so severe that it kills the mouse. The researchers want to know more about what these proteins do and how viral infection causes their production.

“We’re trying to develop a model that describes cytokine production in response to a viral infection and fit that model to mouse data,” says Wilcox.

“Health is pretty important to me,” she says.

Last summer, she and her fiancé – Jon Waito, a DVM student and zoology grad — cycled from Victoria back to Ontario. They had planned to cross Canada but had to halt the trip six weeks in, when Waito crashed his bike and broke his elbow near Sault Ste. Marie.