The Last Frontier of Mathematics

Thursday, January 21, 2021

“Math and medicine are like the two solitudes,” reflected Professor Siv Sivaloganathan, chair of the Department of Applied Mathematics. “They represent two separate cultures and ways of thinking.” When the two combine into mathematical medicine, the results are nothing short of astonishing.

In 1988, Sivaloganathan was a newly minted professor at the University of Alberta.

He enjoyed the work but not the location, so he began to search for openings back in the UK, where he had completed a postdoctorate at Oxford University. In a serendipitous turn of events, he went to an applied math meeting in Newfoundland and met a Waterloo professor who encouraged him to apply for a position in the Faculty of Mathematics. “I was drawn to the atmosphere at Waterloo immediately,” remembered Sivaloganathan. “The Faculty was full of researchers who were pursuing directions that weren’t typical in most academic settings.”

Sivaloganathan’s decision to move to Waterloo in 1994 paid off in more ways than one. In the first year after he moved, he met his wife, a physician whose experiences steered him toward the burgeoning field of mathematical medicine. “One day she told me about a neurosurgery seminar she attended,” he shared. “When I heard about the challenges presented by the speaker, a junior neurosurgeon, I realized this was an area that was crying out for math.”

That speaker, now the chief neurosurgeon at Sick Kids Foundation, agreed to combine forces with Sivaloganathan to identify the best placement for a shunt in children with hydrocephalus. By dissecting the mathematical underpinnings of the existing literature on hydrocephalus, Sivaloganathan was able to construct more effective mathematical models to inform clinical treatment.

Encouraged by the success of his first collaboration, Sivaloganathan began working with the chief medical oncologist at Princess Margaret Cancer Centre to apply math to cancer research. The Centre was running a 10-year clinical trial to determine the most effective sequencing of therapies for ovarian cancer. Using a simple, ordinary differential equation model, Sivaloganathan—together with Mohammad Kohandel, a then-postdoctoral student who is now a faculty member in Applied Math—discovered the most effective sequencing strategy. “My work has sort of mushroomed from that point,” said Sivaloganathan. “There was so much low-hanging fruit, so many problems that had never been modeled mathematically. It was clear to me that medicine was the last frontier for mathematics.”

In 2004, Sivaloganathan and the chief medical oncologist at the Princess Margaret Cancer Centre co-founded the Centre for Mathematical Medicine at the Fields Institute to create a nexus for biomedical engineering, mathematics, and statistics. In the past 17 years, the Centre has brought together applied mathematicians and medical scientists from the world’s top institutions to tackle the most pressing medical questions of our time.

This year, Sivaloganathan is focusing most of his research on high-intensity ultrasound as a therapeutic tool. High intensity focused ultrasound waves (HIFU) have the potential to ablate tumours and other harmful tissues with negligible side effects compared to surgery, chemotherapy, and other standard therapies. “I’ve always said that Waterloo is a place where people think completely outside of the box,” he reflected. “We are encouraged to pursue ideas that will make an impact 10 years down the line. In many ways, Waterloo is the reason that mathematical medicine has gained a foothold in Canada.”

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