Home stretch | Understanding cancer through math

A journey from biology to mathematics and back is the title of his dissertation. It aptly captures the path Mike van Santvoort has taken during his PhD research. A mathematician by training, he found himself immersed in the world of biology, where he explored cancer cells, immune cells, and the ways in which they behave.

It was quite a leap, he admits. But above all, it was an interesting one. “One of the reasons I decided to do it is that it’s an incredibly fascinating problem,” he says. “I thought it was really cool to learn so much about it during my PhD and to work together with biologists.”

A common language

But collaboration across different disciplines doesn’t happen automatically. “One of the challenges is that you have to find a common language. I had to learn to understand what the problem was and exactly what the biologists needed. In turn, I had to convince them that my mathematical models were relevant. Anything new and complicated-looking doesn’t immediately inspire confidence.”

Until then, the biologists had largely relied on machine-learning models to make predictions. These models are powerful, but they have one major drawback: they operate as a black box. They process a lot of input and produce a prediction, without making clear how they arrived there. “I wanted to develop models that not only make predictions, but also provide insight into how they got there.”

When cancer develops

So what exactly is the problem he is tackling? Van Santvoort is not only a mathematician but also trained as a mathematics teacher—a combination that has proved useful during his PhD. “I enjoy explaining complicated things to other people in a simple way,” he says. He takes us to the moment when cancer develops.

“When a cancer cell emerges, it can start dividing very rapidly, causing a tumor to form,” he begins. “But your body has all kinds of mechanisms to prevent that. For example, it often recognizes that a cell has mutated and quickly destroys it. And if a tumor does develop, the immune system can recognize the cancer cells and try to eliminate them.

“The problem arises when cancer cells start defending themselves against this response. They produce certain proteins that help suppress the immune system. You can compare it to a social network. The cancer cells start behaving in a way that makes everyone else think: these are normal cells behaving properly, we should leave them alone.”

Take it easy

One way they do this, is by using a protein called PD-L1. “It’s like a little stub on the membrane of a cancer cell that sends a signal that essentially says: take it easy, there’s nothing wrong here.” Immune cells are, after all, quite aggressive. 

Traditionally, biologists study individual interactions to determine which proteins are responsible for sending that message and thereby weakening the immune response.

“Once we know that, we can use immunotherapy. There are many different types, but the basic idea is that we specifically block the message sent by cancer cells, allowing the immune system to do its job undisturbed and clear out the cancer cells.”

The challenge—and the point where Van Santvoort’s own research begins—is that cancer cells can use many different ‘words’ to deceive the immune system. “We can analyze those very well individually, but in my research I’m trying to develop models of how the entire network of cells functions. Rather than looking only at individual interactions, we study a very large group of cells and how they communicate with one another.”

Better predictions

The mathematical approach he uses is called random graphs. In this branch of mathematics, networks are constructed based on random choices, much like rolling a die. 

“My models were specifically developed for this problem and applied to data from real patients. Based on a biopsy, we can see which genes are activated in the tissue. We use that information to try to build a network of cells and determine how they influence one another. We can then predict which type of immunotherapy is most likely to work for a particular patient.”

But the models can do more than make predictions. “We can also look at which communication patterns are associated with a patient having a worse outcome. That can help us identify new proteins or cells that may play a role. So the model doesn’t just have predictive value; it can also generate new ideas for research.”

Building a bridge

Van Santvoort’s dissertation primarily provides fundamental insights, both for mathematics and for biomedical engineering. The next step is to further validate his models and translate them into clinical practice. In the coming years, that task will fall to his colleagues in biomedical engineering.

For the PhD candidate, the greatest satisfaction lies in connecting two worlds. “Sometimes I felt a bit like an idiot, because I was sitting right between mathematics and biology. In biomedical engineering, I was an outsider, but among the more fundamental mathematicians, I didn’t feel completely at home either. The fact that I ultimately managed to build that bridge and translate mathematics into biology, really does feel like an achievement.”

This article was translated using AI-assisted tools and reviewed by an editor.