Mathematicians Look at the Human Body

Dr Klas Modin will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Computational Mathematics Group at the Department of Mathematical Science, Chalmers University of Technology and the University of Gothenburg.

Computational anatomy is a new branch of mathematics which uses mathematical methods to analyze three-dimensional images of the human body. There are several applications of computational anatomy, but the most important ones are in medicine.

For example, one could try to analyze a three-dimensional MRI image of a heart in order to help a cardiologist identify clinical pathologies. Such an analysis would compare healthy organs to diseased ones and detect differences. One complication here is that healthy human hearts vary broadly in size and form. Therefore, one converts the image into a normalized form first, and then one compares the details to a normalized image of a healthy heart to detect the differences.

Computational anatomy has not reached such a goal yet. Even though the first attempts to describe human organs in mathematical terms were made a hundred years ago, better models and computational methods are necessary in order to develop stable and reliable methods for computational anatomy.

One of mathematical tools successfully applied to computational anatomy is the theory developed for finding the minimal distance between two points of a curved surface. It is related to fluid dynamics and is based on theoretical breakthroughs achieved by the famous Russian mathematician Vladimir Arnold in the 1960’s. Along with the tools of fluid dynamics the project is going to apply methods of other fields of mathematics as well.