**Electrical Impedance Tomography**

## The Kate Edger Department of Mathematics

# Electrical impedance tomography

Electrical impedance tomography (EIT) is a diffuse tomographic modality in which electric currents are injected into a volume conductor and the resulting potentials on the surface are measured. Based on this information, the internal conductivity (resistance) of the object can be reconstructed. Conductivity as such, is seldom interesting, but it often correlates with other quantities such as blood circulation, concentration of chemical substances and air mixed in fluids.

EIT is used for example in biomedical, industrial and geophysical applications. Our main interest has been in the Bayesian modelling and inference aspects of EIT. A central topic is the modelling of uncertainties that often include boundary data. We are particularly well known for imaging of fast phenomena with which conventional imaging methods may fail completely. The related approaches often involve modelling of several coupled stochastic partial differential equations.

Currently, we are concentrating on further modelling of the missing boundary data and the Bayesian model selection problem, as well as several related industrial an

### Researchers at The University of Auckland

### Other collaborators

- Professor Marko Vauhkonen

University of Eastern Finland, Department of Physics and Mathematics. - Doctor Ville Kolehmainen

University of Eastern Finland, Department of Physics and Mathematics. - Aku Seppanen

University of Eastern Finland, Department of Physics and Mathematics. - Doctor Stefan Finsterle

Lawrence Berkeley National Laboratory, Earth Sciences Division - Professor Samuli Siltanen

University of Helsinki, Department of Mathematics

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**