Math may lead to new answers for Parkinson's disease

by Joy Poliquin

Edwards

What do biology and Parkinson's disease have in common with mathematics? For UVic mathematician Dr. Rod Edwards, this combination is the key to unlocking new answers to old problems about the debilitating disease.

Edwards is the applied mathematician on a team of experts from Brock University and the University of Western Ontario who are studying the mathematical properties of Parkinsonian dyskinesias (undesirable involuntary movements), thanks to a $49,800 grant from the Parkinson Society of Canada.

Edwards will analyse the medical data recorded by his colleagues using mathematical concepts from nonlinear dynamics.

Edwards has previously worked with neuroscientists and physiotherapists on other symptoms of Parkinson's disease, such as tremor. In this case, for example, he applied mathematical techniques to precise recordings of finger tremors to define and catch the subtle differences between normal tremor in a healthy individual and the minor tremor that indicates an early stage of Parkinson's.

"Using the math, we could pick up on subtle differences that might not be detectable by a trained clinician," he says.

Edwards developed simple model equations to represent interactions between the structures in the brain that comprise our motor circuitry and control movement.

"If you take the system of equations representing a healthy person's motor circuitry, in which the activity is small and irregular, and then ‘damage' part of this system, you typically see the mathematical equivalent of Parkinsonian tremor, which is a much more regular oscillation."

Edwards' research may lead to earlier detection of the disease and a better understanding of how the neuromotor system is affected. "With a mathematical approach we can describe this disease and its symptoms in new ways," he says. "The new project on diskinesias is in its early stages, but it looks promising."

Edwards has also worked as an applied mathematician on a study involving the movement problems of people with Down Syndrome. He's optimistic about the continuing development of applications of math in the biological world.

"Mathematical biology and physiology are ripe for exploration," he says. "While biochemists, biologists and medical researchers can extract vital information about structures or components, the networks of interaction between these components are often complex and math is a useful tool to understand how they work.

"People often think that abstract math is unapplicable to the real world," he adds. "But when the same abstract patterns underlie many different phenomena, math can offer fundamental insights and new ways to look at the world."