How math is revolutionizing medicine

Friday, November 20, 2020

Clinical trials in medicine are slow, expensive, and most fail. Can mathematical models help us find life-saving drugs faster and more efficiently?

Anita Layton is a Canada 150 Research Chair for her work in Mathematical Biology and Medicine and a member of the Department of Applied Mathematics at the University of Waterloo. She is also a WIN member. Recently, she hosted a panel discussion on math in medicine as part of the University of Waterloo’s Alumni Black and Gold Day at Home celebrations. The following is an excerpt from her opening remarks. The full discussion can be viewed here.

“Only about 3.4% of cancer drug trials are successful. For Alzheimer's, only 0.6% of drug trials are successful.

The lack of a breakthrough in Alzheimer's treatment is particularly frustrating for me, because my husband has Alzheimer's disease.

One piece of advice that you often get as a caregiver of an Alzheimer’s patient is to enroll them in a clinical trial. I mean, it isn't like it can get any worse.

My husband's new oncologists accepted him into a big phase three trial involving some 1500 participants from all over the world. I knew the odds. I knew that participating in a clinical trial was really unlikely to help my husband, but it gave us hope. If you have had a loved one suffering from a horrible terminal disease, you may understand how it makes you grasp at the tiniest straws of hope.

Unfortunately, in situations like this, hope is often very cruel. A year later, the oncologists email me to tell me that the drug company had cancelled his once-promising trial because the drug can actually make you worse.

I felt like I was punched in the stomach. I mean, that was a rather difficult week already. A few days before I got that email, I realized that my husband no longer recognized our engagement ring—the beautiful ring he spent so much time designing that he ended up proposing to me without a ring.

And that was just the beginning, the beginning of what the disease can do. These days, he no longer recognizes me or our children.

One reason that an Alzheimer's drug candidate fails is because it targets the wrong pathological substrate. In the last decade, almost all Alzheimer's drug development has focused on amyloid-beta plaques and the subsequent elimination. Different drug candidates target different isoforms, or variants of amyloid beta, and different terminants or ends of the protein. There are quite a number of combinations.

On top of that, for each pair of isoform and terminus, you can target them using several different compounds. The question is: how can we find the right target and the right compound?

We can be really diligent and try all possible combinations. But there are two problems with this approach. One, some of these compounds are probably very toxic and may kill the patient. Two, to try all possible compounds would take a lot of clinical trials, which means a lot of money. Can we actually convince somebody to pay for it?

This is where mathematical modelling comes in.

We can use a mathematical model to simulate how different molecular pathways respond to the drug and how the target organ or system functions are subsequently affected. And how other organs may be indirectly affected. So that way, the model can predict how effective the drug is, and what the optimal dosages are, and whether the drug has any undesirable side effects.

The good thing about a computer model is that even if the drug destroys the lungs, the model won't die, and it's not going to sue you.

Is a mathematical model perfect? Of course not. It cannot replace a clinical trial. But it can sound an alarm. If the model predicts serious liver toxicity, you probably want to think twice before testing it on patients.

Medical models can also identify promising drug candidates. Let's say you have 20 drug candidates for Alzheimer's. Because it can cost up to $2.5 billion if a drug candidate fails in a phase three trial, it is going to be a tough sale to convince any pharmaceutical company to test all 20 drugs. It is much, much cheaper to run simulations for all 20 candidates, identify the top performers in terms of efficacy and safety, and then run clinical trials only on those top performers.”

To learn more about the Faculty of Math’s research in math and medicine, visit this page.

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