A richer view of the inside

Our ability to see inside a person's body, without surgery, has revolutionised modern medicine and saved countless lives. And each life saved is thanks to the mathematics of tomography. This medical imaging technique passes waves through a person's body, mathematically reconstructing an image from the amount these waves are scattered or absorbed by the structures inside. And tomography isn't just important in medicine. Tomography is also used for many other non-medical purposes – from electron tomography of viruses and microchips to muon tomography of volcanoes.

The field of rich tomography promises an even richer view – more complex measurements offer the opportunity to reconstruct far more detailed structures of the interior of objects – but new mathematics is needed. This is why mathematicians and statisticians working on these problems, came together with the engineers, physicists and clinicians producing and using this tomographic data in the research programme on Rich and Nonlinear Tomography (RNT) at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. As well as being a fascinating example of the power of mathematics to change our lives, this INI programme also demonstrates the power of bringing people together to create new and exciting mathematics.

Saving lives: The mathematics of tomography – Find out about the maths of tomography and the impact it's had on our lives.

A richer view of the inside — The mathematics of tomography has revolutionised modern medicine and many other fields. Find out more about this INI programme and how new mathematics can give us an even better view.

Multiple wave scattering — Tomography uses waves to reconstruct information about the interior of objects. And when many waves meet multiple objects things can get very complex indeed. The RNT programme benefited from running alongside another INI programme on just this topic. Find out more about the fascinating ideas involved.

Maths in a minute: Non-linearity — Non-linear relationships are tricky relationships. Find out why here.

Maths in a minute: Inverse problems — Inverse problems lie at the heart of tomography. Find out about these mathematical detective problems in this brief and accessible article.

Model behaviour — To mathematically understand any system, from reconstructing medical images to understanding the spread of a disease, you need to build a mathematical model. This article gives you a guide to this process and how you might begin to deal with tricky ideas like non-linearity.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.