Cancer is not just a biological problem. It is also a mathematical one. Tumours grow, compete for oxygen, respond to drugs, and adapt to stress — all in ways that can be described, modelled, and predicted using mathematics. Mathematical oncology is the field that does exactly this.

What does a mathematical oncologist actually do?

At its core, mathematical oncology uses equations to describe how cancer behaves. Just as engineers use mathematics to predict how a bridge will hold weight, or meteorologists use it to forecast weather, mathematical oncologists use it to predict how a tumour will grow, shrink, or resist treatment.

The tools vary — differential equations, statistical models, computational simulations — but the goal is the same: turn biological complexity into something we can reason about precisely.

My research: phase-field models of tumour growth

My PhD research focuses on a specific approach called phase-field modelling. Think of it like a weather forecast for a tumour — instead of predicting rain, we predict where cancerous tissue will grow, how it will respond to a drug like paclitaxel, and what happens when oxygen runs low.

The model tracks four key things simultaneously:

  • Tumour volume — how much of a region is cancerous tissue
  • Oxygen levels — tumours starved of oxygen behave very differently from well-supplied ones
  • Drug concentration — how paclitaxel spreads through tissue and kills cells
  • Mechanical stress — physical forces inside and around the tumour affect how it grows

These four things interact constantly. Oxygen shortage triggers different growth patterns. Drug concentration determines how many cells die. Mechanical stress can slow or redirect growth. The mathematics captures all of these interactions together, in a single unified model.

Why does this matter?

Cancer treatment today is largely based on population averages. A drug works for 60% of patients — but which 60%? A standard dose is recommended — but is it right for this particular tumour, in this particular patient?

Mathematics can help answer these questions. By building models that are personalised to a patient's specific tumour characteristics, we move closer to treatment that is tailored to the individual rather than the average.

This is not science fiction. Mathematical models are already informing treatment planning in radiation therapy. The next frontier is bringing the same rigour to chemotherapy, immunotherapy, and combination treatments.

The road ahead

Mathematical oncology is a young field, but it is growing fast. As biological data becomes richer and computing power increases, the models become more accurate and more useful.

The goal is not to replace oncologists. It is to give them sharper tools — to help them see what is happening inside a tumour, predict what will happen next, and choose the treatment most likely to work.

That is the problem I work on every day. And it is one worth solving.