These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics students. Coffee, tea and drinks will be provided.
 
 

Positron Emission Tomography (PET) is a remarkable medical imaging modality. Rather than showing anatomical structure like a CT scan (or x-ray), a PET scan shows functional structure. However, the mathematics involved in PET has much in common with CT and MRI.

In PET, the patient is injected with a pharmaceutical tagged with a radioactive isotope (a positron emitter). The patient then lies in a PET scanner for a while - sometimes a very long while, I will come back to this - and radioactive decay events are detected and sorted into two dimensional projections. Images reconstructed from these projections show the distribution of the absorption of the pharmaceutical by cells in the body. For example, malignant cancer cells absorb more glucose than normal cells because they grow more prodigiously; they will appear bright in a PET scan. Damaged brain cells absorb less oxygen than healthy ones, so they will appear darker.

In this talk I will explain how PET works, in particular how positron emissions are converted to two dimensional projections and how these are reconstructed mathematically. A PET scan can take up to two and a half hours. This is pretty unpleasant for someone who is really sick. I will discuss how a bit of simple maths can speed up patient scan times. I will also touch on some of the issues working as a mathematician or physicist in a hospital.