UW researchers use mathematical models to analyze the use of ultrasound to target tumours

Graphic by Jia Chen

Researchers at the University of Waterloo are using mathematical models to analyze the use of ultrasound to target cancerous tumours.

About eight years ago, Dr. James Drake, the chief surgeon at the Hospital for Sick Children, approached the biomedical research group at the University of Waterloo with the proposal to look into the uses of High-Intensity Focused Ultrasound (HIFU) for treatment of tumours and lesions. 

“Ultrasound has been around in medicine for a long while, but it is usually the low frequency kind that is being used in medical imaging,” said Siv Sivaloganathan, head of the biomedical research group in the Department of Applied Mathematics at UW. “The last decade or two, we are suddenly interested in high frequency ultrasound which carries a lot more energy. If you focus the ultrasound using a transducer, you can destroy the tumor at that point.”

According to Sivaloganathan, using ultrasound to destroy tumours would be a huge advancement for treatment since the patients are not subject to side effects associated with radiation or chemotherapy, and no follow-up medications would be required.  

Sivaloganathan, along with co-authors Messoud Efendiyev, named the 2019 James D.Murray Distinguished Visiting Professor, as well as UW graduate student June Murley, published a paper titled, “Dimension estimate of uniform attractor for a model of high intensity focussed ultrasound-induced thermotherapy,” which outlines the process as a simple model using a simple linear equation — a combination of a wave equation and a heat equation. 

“The only problem that crops up, is in the process of focusing the ultrasound is that there will be energy deposited in healthy tissue, though not as much as at the focal point,” Sivaloganathan said. “The [goal] is to try and balance the absorbance of energy in healthy tissue so that you don’t elevate the temperature in normal tissue too much. You can do that in many ways – one of the ways is using Pulsed High-Intensity Focused Ultrasound, so you periodically use it for certain amounts of time.”

In order to monitor the temperature of the surrounding tissue, HIFU is used in conjunction with Magnetic Resonance Imaging (MRI). It is difficult to measure the temperature within bone, therefore when the tumour is on bone, it is unknown how the bone marrow may be negatively affected. 

The research team aims to find a solution to this problem using mathematical models and computational solutions in conjunction with clinical observations.

The use of ultrasound on tumors has been previously accomplished at the Hospital for Sick Children in Toronto by interventional radiologist Dr. Michael Temple. HIFU was used successfully on a youth with an osteoid osteoma, a benign bone tumour, in his leg. This technique allowed for the patient, who had been in excruciating pain, to avoid surgery and instead undergo a 30-minute procedure resulting in no complications, quick recovery and no additional pain.

HIFU technology also has many other possible medical applications. The research group is also interested in looking into its uses to disrupt blood clots and deliver drugs across the blood-brain barrier. 

Since there have been successes in the past using HIFU on benign tumours, there are high hopes for the research being done at UW and that the technology will be able to be applied to cancerous tumours as well. 

Home to one of the only mathematical biology labs, UW is uniquely equipped to tackle this project and provide mathematical solutions that will hopefully form the path toward clinical trials.